Methodology for design and operations of field-wide and multi-well enhanced oil recovery of unconventional hydrocarbon assets

ABSTRACT

A methodology using an interwell connectivity model for hydrocarbon management is disclosed. The interwell connectivity model may include interwell connectivity metrics indicative of fluid interconnectivity amongst pairs of wells and may be used as predictive or prescriptive for enhanced oil recovery (EOR). As predictive, the interwell connectivity model may be used to determine an effect of gas injection into the reservoir on one or more aspects of EOR, such as reservoir pressure or production rates. As prescriptive, the interwell connectivity model may be used to improve or optimize various stages of EOR, such as during drilling or construction of the extraction site, during primary depletion, or during one or more huff-and-puff cycles.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application Ser. No. 63/368,690, entitled “METHODOLOGY FOR DESIGN AND OPERATIONS OF FIELD-WIDE AND MULTI-WELL ENHANCED OIL RECOVERY OF UNCONVENTIONAL HYDROCARBON ASSETS,” filed Jul. 18, 2022, and the benefit of U.S. Provisional Application Ser. No. 63/368,692, entitled “METHODOLOGY FOR DESIGN AND OPERATIONS OF FIELD-WIDE AND MULTI-WELL ENHANCED OIL RECOVERY OF UNCONVENTIONAL HYDROCARBON ASSETS,” filed Jul. 18, 2022, the disclosures of which are hereby incorporated by reference in their entirety.

FIELD OF THE INVENTION

The present application relates generally to the field of hydrocarbon exploration, development and production. Specifically, the disclosure relates to a methodology for design and operations of field-wide and multi-well enhanced oil recovery (EOR) of unconventional hydrocarbon assets.

BACKGROUND OF THE INVENTION

This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present disclosure. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present disclosure. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.

Hydrocarbon production from tight-oil bearing rocks (e.g., unconventional resources) is almost exclusively via primary depletion, which may leave approximately 90% of the oil in place behind. Enhanced oil recovery (EOR) represents a leading set of technologies to improve oil recovery from unconventional resources. In particular, fluid injection, such as nitrogen injection for reservoir pressure maintenance or carbon dioxide injection for miscible flooding for EOR, may be used. See U.S. Pat. No. 8,984,857, incorporated by reference herein in its entirety. See also US Patent Application Publication No. 20170136401 A1; US Patent Application Publication No. 20170138222 A1; US Patent Application Publication No. 20190322921 A1, each of which are incorporated by reference herein in their entirety.

SUMMARY OF THE INVENTION

In one or some embodiments, a computer-implemented method for enhanced oil recovery (EOR) for a plurality of wells in one or more intervals is disclosed. The method includes: accessing an interwell connectivity model comprising interwell connectivity metrics indicative of fluid interconnectivity amongst at least pairs of wells in the plurality of wells, the interwell connectivity model including controllable one or more inputs for inputting gas into a reservoir and one or more outputs related to EOR; and controlling, based on the interwell connectivity model, the one or more inputs for EOR.

In one or some embodiments, a method for hydrocarbon extraction is disclosed. The method includes: accessing an interwell connectivity model that is indicative of fluid connectivity of a plurality of wells; determining, based on the interwell connectivity model, one or more aspects of one or both of control or configuration of the plurality of wells; and using the one or more aspects of one or both of control or configuration of the plurality of wells for hydrocarbon management of a reservoir.

BRIEF DESCRIPTION OF THE DRAWINGS

The present application is further described in the detailed description which follows, in reference to the noted plurality of drawings by way of non-limiting examples of exemplary implementations, in which like reference numerals represent similar parts throughout the several views of the drawings. In this regard, the appended drawings illustrate only exemplary implementations and are therefore not to be considered limiting of scope, for the disclosure may admit to other equally effective embodiments and applications.

FIG. 1A illustrates a schematic of the analytical model for a 3-well system with an injector well, surrounded by two offset producer wells.

FIG. 1B is a top view of 12 horizontal hydraulically fractured wells showing fluid transport from the injection wells, including well #16 for 30 days followed by well #14 for 30 days, to its neighboring wells based on stress orientation within the subsurface.

FIG. 1C illustrates a 3-D configuration showing fluid transport from the injection well to neighboring wells in multiple reservoir intervals.

FIG. 2A is a block diagram of the analytical model.

FIG. 2B is a block diagram of the design and operational mechanism, including the analytical model of FIG. 2A.

FIG. 3A is a graph of output of the analytical model predicting bottomhole pressure over time for wells #1, #2, #3, #4, #5, and #18.

FIG. 3B is a graph of output of the analytical model predicting bottomhole pressure over time for wells #13, #14, #15, #16, #29, and #6.

FIG. 4 is a graph of the percent of injectant leaking out of the area of interest as a function of time and injection rate.

FIG. 5A is a graph of oil production rates (barrels/day) over time for wells #1, #2, #3, #4, #5, and #18.

FIG. 5B is a graph of oil production rates (barrels/day) over time for wells #13, #14, #15, #16, #29, and #6.

FIG. 6 is a schematic indicating instantaneous bottomhole pressure response in the injector well (P₁) and delayed pressure response in an offset well (P₂) due to change in injection rate in the injector well (P₁).

FIG. 7 is a graph of interwell conductivity (F) versus average bottomhole pressure (P_(avg)) for buildup and drawdown.

FIGS. 8A-C illustrate top views of three different scenarios for distribution of hydraulic fractures for two horizontal wells, including hydraulic fractures in the two horizontal wells that do not hit each other (FIG. 8A), hydraulic fractures in the two horizontal wells that do hit each other (FIG. 8B), and hydraulic fractures in the two horizontal wells that are zippered or intermingled (FIG. 8C).

FIG. 9A is a block diagram of a system model that includes parts for an analytical model and an optimization model, with the system model being used in one or more stages of EOR, including the design stage, the primary depletion stage, and the gas injection stage (e.g., one or more huff and puff stages).

FIG. 9B is a block diagram of the design model for optimization during the design stage.

FIG. 9C is a block diagram of the operations model for optimization during one or more operation stages, such as the primary depletion stage and/or the gas injection stage.

FIG. 9D is a block diagram of the huff and puff system.

FIG. 10 is a graph of hydrocarbon extraction from an injector well versus time in the primary depletion stage and the huff and puff stage (including multiple cycles of huff and puff in the injector well), and block diagrams of the model calibration of the reservoir model in the various stages.

FIG. 11 is a graph of hydrocarbon extraction from an offset well (that is not plugged during huffing) versus time in the primary depletion stage and the huff and puff stage (including multiple cycles of huff and puff in the injector well), and block diagrams of the model calibration of the reservoir model in the various stages.

FIG. 12 is a graph of hydrocarbon extraction from both injector well(s) and offset well(s) versus time in the primary depletion stage and the huff and puff stage (including multiple cycles of huff and puff in the injector well(s)), and block diagrams of the model calibration of the reservoir model in the various stages.

FIGS. 13A-C are illustrations showing different stages of operation of a well, including during production without any gas injection (e.g., no gas injection through the tubing and no gas injection in the annulus) shown in FIG. 13A, during production with artificial lift (e.g., gas injected into the annulus) shown in FIG. 13B, and during gas injection through the tubing (e.g., huff) shown in FIG. 13C.

FIG. 14A is a block diagram of the system design for the multiple optimization models.

FIG. 14B is a block diagram of inputs to and outputs from the analytical model.

FIG. 15 is flow diagram for optimization in one or more stages, including the design stage and the huff and puff stage.

FIG. 16 is a flow diagram for optimization, accounting for uncertainty using conditional value-at-risk (CVaR) net present value (NPV).

FIG. 17 is a representation of an injector well, an offset well and the reservoir.

FIG. 18 is a diagram of an exemplary computer system that may be utilized to implement the methods described herein.

DETAILED DESCRIPTION OF THE INVENTION

The methods, devices, systems, and other features discussed below may be embodied in a number of different forms. Not all of the depicted components may be required, however, and some implementations may include additional, different, or fewer components from those expressly described in this disclosure. Variations in the arrangement and type of the components may be made without departing from the spirit or scope of the claims as set forth herein. Further, variations in the processes described, including the addition, deletion, or rearranging and order of logical operations, may be made without departing from the spirit or scope of the claims as set forth herein.

It is to be understood that the present disclosure is not limited to particular devices or methods, which may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” include singular and plural referents unless the content clearly dictates otherwise. Furthermore, the words “can” and “may” are used throughout this application in a permissive sense (i.e., having the potential to, being able to), not in a mandatory sense (i.e., must). The term “include,” and derivations thereof, mean “including, but not limited to.” The term “coupled” means directly or indirectly connected. The word “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any aspect described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects. The term “uniform” means substantially equal for each sub-element, within about ±10% variation.

The term “seismic data” as used herein broadly means any data received and/or recorded as part of the seismic surveying and interpretation process, including displacement, velocity and/or acceleration, pressure and/or rotation, wave reflection, and/or refraction data. “Seismic data” is also intended to include any data (e.g., seismic image, migration image, reverse-time migration image, pre-stack image, partially-stack image, full-stack image, post-stack image or seismic attribute image) or interpretation quantities, including geophysical properties such as one or more of: elastic properties (e.g., P and/or S wave velocity, P-Impedance, S-Impedance, density, attenuation, anisotropy and the like); and porosity, permeability or the like, that the ordinarily skilled artisan at the time of this disclosure will recognize may be inferred or otherwise derived from such data received and/or recorded as part of the seismic surveying and interpretation process. Thus, this disclosure may at times refer to “seismic data and/or data derived therefrom,” or equivalently simply to “seismic data.” Both terms are intended to include both measured/recorded seismic data and such derived data, unless the context clearly indicates that only one or the other is intended. “Seismic data” may also include data derived from traditional seismic (e.g., acoustic) data sets in conjunction with other geophysical data, including, for example, gravity plus seismic; gravity plus electromagnetic plus seismic data, etc. For example, joint-inversion utilizes multiple geophysical data types.

The term “geophysical data” as used herein broadly includes seismic data, as well as other data obtained from non-seismic geophysical methods such as electrical resistivity. In this regard, examples of geophysical data include, but are not limited to, seismic data, gravity surveys, magnetic data, electromagnetic data, well logs, image logs, radar data, or temperature data.

The term “geological features” (interchangeably termed geo-features) as used herein broadly includes attributes associated with a subsurface, such as any one, any combination, or all of: subsurface geological structures (e.g., channels, volcanos, salt bodies, geological bodies, geological layers, etc.); boundaries between subsurface geological structures (e.g., a boundary between geological layers or formations, etc.); or structure details about a subsurface formation (e.g., subsurface horizons, subsurface faults, mineral deposits, bright spots, salt welds, distributions or proportions of geological features (e.g., lithotype proportions, facies relationships, distribution of petrophysical properties within a defined depositional facies), etc.). In this regard, geological features may include one or more subsurface features, such as subsurface fluid features, that may be hydrocarbon indicators (e.g., Direct Hydrocarbon Indicator (DHI)). Examples of geological features include, without limitation salt, fault, channel, environment of deposition (EoD), facies, carbonate, rock types (e.g., sand and shale), horizon, stratigraphy, or geological time, and are disclosed in US Patent Application Publication No. 2010/0186950 A1, incorporated by reference herein in its entirety.

The terms “velocity model,” “density model,” “physical property model,” or other similar terms as used herein refer to a numerical representation of parameters for subsurface regions. Generally, the numerical representation includes an array of numbers, typically a 2-D or 3-D array, where each number, which may be called a “model parameter,” is a value of velocity, density, or another physical property in a cell, where a subsurface region has been conceptually divided into discrete cells for computational purposes. For example, the spatial distribution of velocity may be modeled using constant-velocity units (layers) through which ray paths obeying Snell's law can be traced. A 3-D geologic model (particularly a model represented in image form) may be represented in volume elements (voxels), in a similar way that a photograph (or 2-D geologic model) may be represented by picture elements (pixels). Such numerical representations may be shape-based or functional forms in addition to, or in lieu of, cell-based numerical representations.

The term “subsurface model” as used herein refer to a numerical, spatial representation of a specified region or properties in the subsurface.

The term “geologic model” as used herein refer to a subsurface model that is aligned with specified geological feature such as faults and specified horizons.

The term “reservoir model” as used herein refer to a geologic model where a plurality of locations have assigned properties including any one, any combination, or all of rock type, EoD, subtypes of EoD (sub-EoD), porosity, clay volume, permeability, fluid saturations, etc.

For the purpose of the present disclosure, subsurface model, geologic model, and reservoir model are used interchangeably unless denoted otherwise.

Stratigraphic model is a spatial representation of the sequences of sediment, formations and rocks (rock types) in the subsurface. Stratigraphic model may also describe the depositional time or age of formations.

Structural model or framework results from structural analysis of reservoir or geobody based on the interpretation of 2D or 3D seismic images. For examples, the reservoir framework comprises horizons, faults and surfaces inferred from seismic at a reservoir section.

As used herein, “hydrocarbon management” or “managing hydrocarbons” includes any one, any combination, or all of the following: hydrocarbon extraction; hydrocarbon production, (e.g., drilling a well and prospecting for, and/or producing, hydrocarbons using the well; and/or, causing a well to be drilled, e.g., to prospect for hydrocarbons; and/or hydrocarbon injection); hydrocarbon exploration; identifying potential hydrocarbon-bearing formations; characterizing hydrocarbon-bearing formations; identifying well locations; determining well injection rates; determining well extraction rates; identifying reservoir connectivity; drilling and/or construction of wells (including drilling the wells or performing hydraulic fracturing); configuring the well site (including selection of the mechanical hardware, such as the compressor(s), the piping, etc. in support of injecting gas to the well(s) or extracting hydrocarbon from the wells); acquiring, disposing of, and/or abandoning hydrocarbon resources; reviewing prior hydrocarbon management decisions; and any other hydrocarbon-related acts or activities, such activities typically taking place with respect to a subsurface formation. The aforementioned broadly include not only the acts themselves (e.g., extraction, production, drilling a well, etc.), but also or instead the direction and/or causation of such acts (e.g., causing hydrocarbons to be extracted, causing hydrocarbons to be produced, causing a well to be drilled, causing the prospecting of hydrocarbons, etc.). Hydrocarbon management may include reservoir surveillance and/or geophysical optimization. For example, reservoir surveillance data may include, well production rates (how much water, oil, or gas is extracted over time), well injection rates (how much water or CO₂ is injected over time), well pressure history, and time-lapse geophysical data. As another example, geophysical optimization may include a variety of methods geared to find an optimum model (and/or a series of models which orbit the optimum model) that is consistent with observed/measured geophysical data and geologic experience, process, and/or observation.

As used herein, “obtaining” data generally refers to any method or combination of methods of acquiring, collecting, or accessing data, including, for example, directly measuring or sensing a physical property, receiving transmitted data, selecting data from a group of physical sensors, identifying data in a data record, and retrieving data from one or more data libraries.

As used herein, terms such as “continual” and “continuous” generally refer to processes which occur repeatedly over time independent of an external trigger to instigate subsequent repetitions. In some instances, continual processes may repeat in real time, having minimal periods of inactivity between repetitions. In some instances, periods of inactivity may be inherent in the continual process.

If there is any conflict in the usages of a word or term in this specification and one or more patent or other documents that may be incorporated herein by reference, the definitions that are consistent with this specification should be adopted for the purposes of understanding this disclosure.

As discussed in the background, EOR techniques, such as fluid injection, may be difficult to predict due to complex geomechanical processes. In particular, reservoir properties tend to be complex, and may be pressure dependent and/or hysteretic in nature. For example, fluid injected in one or many unconventional wells tends to migrate along hydraulic fractures of the injectors(s) and connect with the fractures of the neighboring wells. In this regard, special capabilities may be used to design an integrated system for improved or optimal hydrocarbon recovery while respecting operational and environmental constraints.

For example, EOR techniques may comprise using gas (e.g., one or both of gas lift or gas injection into the subsurface (e.g., into the reservoir)). Gas may be used to modify the pressure at various parts of the system, such as one or both of within a well (e.g., by using gas lift and/or by modifying the bottomhole pressure through gas injection into the reservoir) or within the subsurface (e.g., at one or more parts of the reservoir within the subsurface). By modifying the pressure (e.g., changing the pressure gradient from the reservoir to one or more bottomholes and/or from the bottomhole to the wellhead), hydrocarbons may be extracted from the reservoir.

In order to perform EOR, one or more models may be used. As one example, reservoir simulation model may be used, such as illustrated in US Patent Application Publication No. 2011/0087471 A1, incorporated by reference herein in its entirety. The reservoir simulation model may be used to generate values for some or all of the potential variables in the subsurface, such as subsurface qualities (e.g., porosity, permeability, etc.) and the effect of injection (e.g., pressure at any point in the subsurface), However, performing a reservoir simulation may necessitate a very high computational cost. As another example, a machine learning (ML) model may be used, such as illustrated in US Patent Application Publication No. 2020/0183047 A1, incorporated by reference herein in its entirety. Again, using an ML model may necessitate a high computational cost.

Thus, in one or some embodiments, a system may comprise an analytical model that is tailored to correlating one or more inputs for EOR with one or more outputs. As one example, any one, any combination, or all of the inputs for EOR, such as one or more aspects related to gas injection (e.g., amount of injected gas, type of injected gas, rate of injected gas, etc.) correlated to any one, any combination, or all of the outputs of EOR, including one or more aspects related to hydrocarbon production (e.g., production rates) and/or one or more aspects associated with the reservoir (e.g., reservoir pressure). As discussed in more detail below, an interwell connectivity metric may be used to correlate the inputs related to gas injection with the outputs related to hydrocarbon production and/or reservoir pressure.

In particular, the disclosed analytical model based on interwell connectivity (interchangeably termed the interwell connectivity model) may be significantly faster (e.g., using the interwell connectivity model may determine pressure in the subsurface in a few hours) than a typical reservoir simulation-based approach (which may take weeks to obtain a history match and to generate a prediction). Thus, in one embodiment, the analytical model is based on well-to-well communication (e.g., the interwell connectivity metric indicative of fluid communication between two or more wells) observed from an EOR field trial, and may therefore be representative of other tight-oil bearing plays/intervals.

In one or some embodiments, the interwell connectivity model may be used to control the one or more inputs for EOR. Merely by way of example, the interwell connectivity model may be used to determine pressure in at least a part of the subsurface, such as in a hydrocarbon reservoir in the subsurface. In particular, the interwell connectivity model may be used to determine the pressure (e.g., the average pressure) in the reservoir based on one or both of an amount of gas injected into the reservoir or a time period of injecting the gas into the reservoir. Alternatively, the interwell connectivity model may be used to determine the inputs needed in order to generate a desired output. For example, the interwell connectivity model may be used to determine one or more aspects of the gas injected (e.g., the amount, the timing, and/or the type) in order to achieve a desired amount of hydrocarbon production and/or a desired amount of pressure in the subsurface (e.g., a desired average pressure in the reservoir). As such, the interwell connectivity model may be used in order to control the inputs (e.g., the gas injected) in order to generate a desired and/or pre-determined pressure profile in one or more parts of the subsurface (e.g., in the reservoir and/or at the one or more bottomholes) in order to perform hydrocarbon extraction.

In this way, various types of EOR may be performed with the effects of the EOR being determined by the interwell connectivity model. For example, one type of EOR is huff and puff, in which during the huff stage, gas is injected via one or more injector wells into the subsurface and thereafter during the puff stage, gas is no longer injected via one or more injector wells into the subsurface. As an analogy, huff and puff is akin to, during the huff stage, blowing air into a balloon and during the puff stage, releasing the air from the balloon. When blowing air into the balloon, the amount of pressure in the balloon increases. Likewise, when injecting gas via the one or more injector wells, pressure increases in the subsurface. In practice, the interwell connectivity model may be used to determine the pressure (such as the average pressure) in the subsurface (such as in the reservoir). Similarly, when releasing air from the balloon, the amount of pressure changes or lowers. Likewise, during the puff, pressure changes in the subsurface, with the interwell connectivity model being used to determine the pressure changes. In one or some embodiments, the interwell connectivity metric may be situationally dependent (e.g., whether building up pressure through huffing or drawing down pressure through puffing) mirroring the pressure dependent and/or hysteretic nature of the subsurface, as discussed further below. In this way, the huff and puff stages may result in pressure changes in the subsurface, with the interwell connectivity model being used to determine the resultant changes in hydrocarbon production rates in one or both of the huff stage or the puff stage.

Separate from being used to determine changes (e.g., production and/or pressure changes) due to gas injection into the subsurface, the interwell connectivity model may be used to determine changes, such as pressure changes and/or production rate changes, when performing gas lift. As discussed in more detail below, gas lift may modify the change in pressure from the bottomhole to the wellhead. In this way, the interwell connectivity model may be used to determine a pressure differential between the reservoir to one or more bottomholes, and may be used in combination with the gas lift (which determines the pressure differential between the one or more bottomholes and the wellheads) in order to provide a holistic approach to pressure (from reservoir to wellhead) in order to extract the hydrocarbons from the reservoir to the wellhead.

Alternatively, or in addition, the interwell connectivity model may be paired with an improvement model or an optimization model in order to control one or more stages of hydrocarbon extraction, such as any one, any combination, or all of: the drilling and construction stage; the primary depletion stage; or the EOR stage (e.g., injecting gas into the tubing as part of huff and puff and/or injecting gas into the annulus as part of artificial lift). More particularly, the interwell connectivity metric may be situationally dependent (e.g., whether building up or drawing down) mirroring the pressure dependent and/or hysteretic nature of the subsurface, as discussed further below.

Thus, in one example, such a system may include any one, any combination, or all of the following components: (1) an analytical model for subsurface response (e.g., the interwell connectivity model); (2) estimating model uncertainty and model tuning for enhancing model predictive capability when new data is available (e.g., updating the model based on data received in a previous stage in order to improve the model for use in subsequent stages); and (3) an improved or optimal design and operational mechanism (e.g., an optimization model for use in selecting one or more parameters in any one, any combination, or all of: the drilling and construction stage; the primary depletion stage; or the EOR stage). In one embodiment, the analytical model, the estimating model uncertainty and model tuning, and the optimization model may comprise separate models. Alternatively, two or all of the analytical model, the estimating model uncertainty and model tuning, and the optimization model may reside within a single model.

Thus, in one or some embodiments, an analytical model (e.g., the interwell connectivity model) is used that is configured to predict and/or forecast one or more metrics related to EOR, such as the subsurface response and/or the use of resources (such as injectant leakage and/or sequestration), to one or multiple stimuli including fluid injection for interconnected well configuration (e.g., one or both of injection well(s) and producing wells). As discussed in more detail below, the analytical model may use any one, any combination, or all of the following in order to determine the EOR metrics: well-to-well connectivity (e.g., an interwell connectivity metric); a number of wells; or configuration of neighboring wells. Example EOR metrics include any one, any combination, or all of: bottomhole pressure (BHP) of one or both of the injector well(s) and offset well(s) during EOR processes; reservoir pressure; amount of injectant leaking out of area of interest; oil production rates; or the like. In turn, the analytical model may use one or more of the EOR metrics in order to generate one or more additional metrics. For example, the analytical model may use BHP in order to predict one or both of oil recovery (e.g., the total oil recovery from the wells in the one or more intervals) and/or the oil uplift (e.g., an indicator of the incremental oil production increase in the one or more intervals) and/or pressure in one or more parts of the subsurface.

Thus, in one or some embodiments, the analytical model, which may be based on interwell connectivity, may be used to predict one or more reservoir properties. Further, various ways are contemplated in order to determine interwell connectivity. In one or some embodiments, interwell connectivity may be generated for a plurality of wells (such as different pairs of wells) and may be indicative of any one, any combination, or all of: physical proximity of the plurality of wells; subsurface indicators (e.g., stress orientation in the subsurface); fluid connectivity (e.g., whether and/or how gas injected into tubing of an injector well travels to an offset well, such as the tubing of the offset well); presence of natural and/or hydraulic fractures connecting wells; and rock properties (e.g., permeability).

As one example, interwell connectivity may be derived or determined based on pressure. In particular, due to complex geomechanical processes, reservoir properties may be pressure dependent and hysteretic in nature. As such, in one or some embodiments, the interwell connectivity may be dependent on pressure. More specifically, the interwell connectivity may be dependent on whether there is a build-up (e.g., increasing pressure) or a draw-down (e.g., decreasing pressure). In this way, the interwell connectivity, as a reflector or indicator of reservoir properties, may be both dependent on pressure and hysteretic in nature. As discussed further below, such a predictive capability may be used in combination with improvement or optimization modeling in one, some, or all of the following: assist in the design and implementation of various aspects of EOR, such as compression/pumping capacity for injection; predict various results (e.g., the amount of injectant leaking to offset wells); and optimize a field implementation of EOR in unconventional reservoirs.

Further, in one or some embodiments, the interwell connectivity model, which may be indicative of the impact of injecting gas on the pressure system on one or more aspects of hydrocarbon extraction, may include use different physics equations depending on one or more aspects of the system. For example, in a first state (e.g., depending on pressure), the gas may be dissolved in the oil in the subsurface, and in a second state (in which the pressure is greater than the bubble point), may not be dissolved in the oil. Each state has an associated set of physics equations to describe the behavior of the gas in the subsurface. In this way, in one or some embodiments, the interwell connectivity model may incorporate the different states and associated equations in determine the effect of injecting gas.

As discussed above, the analytical model may be used in various stages of hydrocarbon extraction, including any one, any combination, or all of the design stage (e.g., drilling and/or construction), primary depletion stage, or gas injection stage (e.g., one or both of gas injected into the tubing as part of huffing or injected into the annulus as part of an artificial lift). In particular, the analytical model may be used in combination with (or as part of) the design and operational mechanism in order to determine improved or optimal EOR in a variety of contexts in hydrocarbon management. As one example, the analytical model may be used as part of an improved or optimal design and operational mechanism that is configured to select improved or optimal option(s) of EOR system design parameter(s). Various types of improved or optimal design and operational mechanisms are contemplated. For example, various models are contemplated as improved or optimal design and operational mechanisms, such as any one, any combination, or all of: design model (which may be used for improvement or optimization for the design stage in determining the drilling and/or construction parameters, such as the number of wells, the placement of wells, the hardware used, etc.); primary depletion model (e.g., which may be used for improvement or optimization for the primary depletion stage in determining various aspects of primary depletion, such as when to end the primary depletion stage); the gas injection model(s) (e.g., one or more models to determine one or both of whether, what, and/or how long to inject gas into the tubing as part of huffing and/or to determine whether, what, and/or how long to inject gas into the annulus as artificial lift). In this regard, the various models, such as the design model, the primary depletion model, and the gas injection model(s) may be used at the various stages of hydrocarbon production. In one or some embodiments, the design model, the primary depletion model, and the gas injection model(s) may comprise separate models. Alternatively, two or more of the design model, the primary depletion model, and the gas injection model(s) may reside within a single model.

In particular, one or more system parameters related to any one, any combination, or all of the design stage, the primary depletion stage, or the gas injection stage may have potential values (such as a range of values) that may be used. The improvement or optimization model may work in combination with the analytical model, due to its predictive nature, to analyze different potential values for the one or more system parameter(s) and to select the values for the one or more system parameter(s), which may in turn be used in the various stages of hydrocarbon extraction. In one or some embodiments, the improvement or optimization model may further include other constraints, such as economic constraints, practical constraints, or the like, in order to identify values for the one or more system parameters. In this way, the design and operational mechanism (which may include the improvement or optimization model and the analytical model) may determine an improved set of values for the one or more system parameters.

As discussed above, the improvement or optimization model may be manifested in a single model for a respective stage (or a respective sub-part of a stage, such as cycle operations model_1 1024, discussed below). For example, a design model may be used for improvement or optimization of parameters in the design stage (e.g., selection of parameters for drilling and construction), a primary depletion model may be used for improvement or optimization of parameters in the primary depletion stage, and one or more gas injection models may be used for improvement or optimization of parameters in the gas injection stage (e.g., one or more models for generating parameters: (i) for huff and puff in the injector well(s) and/or offset wells; and/or (ii) for artificial lift in the injector well(s) and/or the offset wells). Alternatively, the improvement or optimization model may be manifested in a model that spans multiple stages in the hydrocarbon development, such as any two or more of the design stage, the primary depletion stage, or the gas injection stage.

The respective model may be used in combination with the analytical model to analyze different sets of potential values for “N” parameters (e.g., first set of potential values include values for the “N” EOR system design parameters; second set of potential values include values for the “N” EOR system design parameters; etc.). Depending on the respective parameter, the potential values may be discrete (e.g., the number of wells, which may comprise integer numbers); continuous (e.g., temperature, pressure, flow rates, etc. may have associated ranges of potential values); or categorical (e.g., a variable is assigned a value that is not a number). The analytical model, using the values for a respective set of potential values, may predict one or more metrics, such as any one, any combination, or all of the following EOR metrics: bottomhole pressure; amount of injectant leaking out of area of interest; amount of injectant being sequestered in the area of interest; oil production rates; or the like. Based on the one or more metrics, the improved or optimal design and operational mechanism may select an improved (or optimal) set of potential values of the design parameters. As one example, the improved or optimal design and operational mechanism may perform a cost-benefit analysis using the one or more EOR metrics generated by the analytical model in order to select one set of the potential values of the EOR system design parameters. As another example, the improved or optimal design and operational mechanism may weight the one or more EOR metrics generated by the analytical model in order to select one set of the potential values of the EOR system design parameters.

In practice, an optimization algorithm may be used in order to select values for one, some, or each of the parameters at issue. Further, in a first step, initial values for the parameters may be selected. In one or some embodiments, an engineer or the like may select the initial values. Alternatively, the initial values may be automatically selected (e.g., the automatically selected initial values may be presented to the engineer for approval). Still alternatively, the initial values may be selected based on a combination of manual and automatic selections.

In a second step, an algorithm, such as a genetic algorithm or other type of evolutionary algorithm, may input the initial values and be used in order to evaluate and select one or more “best’ solutions. Thus, the algorithm may provide a way in which to consider various physical inputs in determining “best” potential solution(s). Merely by way of example, contemplated algorithms include differential evolution (or other type of evolutionary computation), simulated annealing algorithm, or particle swarm optimization. The algorithm may iterate through various solutions, with the first iteration using the initial values determined in the first step. Thereafter, the algorithm may modify the values of the parameters to identify the defined “best” solution (or a set of “best” solutions). By way of example, the algorithm may randomly populate the space around the initial guesses and evaluate the model for each of the specific combination of inputs, with each iteration biasing more toward an area of the space where the answer tends more to the defined “best” solution.

In one or some embodiments, the “best” solution may be defined in one of several ways, including based on one or more factors. Example factors include, but are not limited to, any one, any combination, or all of: production metrics (e.g., BHP, oil recovery, oil uplift); costs (e.g., material costs (e.g., fluid costs), equipment costs (e.g., pumps or the like); worker costs (e.g., amount of time and/or frequency of monitoring or controlling equipment); or efficiency of the process (e.g., utilization, such as the incremental number barrels of oil produced per volume of injected gas). Other factors may include largest present value (which may be used where a project has unlimited capital) or a largest present value ratio (or the rate or return).

In addition, in one or some embodiments, the factors may be weighted in order to select what is defined as the “best” potential solutions. As one example, oil uplift and material costs may be weighted in order to select the “best” solutions. As another example, oil uplift, material costs, and worker costs may be weighted in order to select the “best” solutions. The engineer may then be presented with the “best” potential solution or the set of “best” potential solutions in order for the engineer to select one solution for implementation. The presentation of the “best” potential solution(s) may further include information on the associated factors. Merely by way of example, a set of potential solutions may be presented to the engineer. Though the algorithm did not factor worker costs in selecting the set of “best” potential solutions, the engineer may be presented with the set of “best” potential solutions along with other information, such as associated worker costs. For example, two potential solutions (selected based on oil uplift) may be presented to the engineer, with a higher-ranked solution requiring more work from workers (e.g., more frequent trips to the field to monitor the wells) or more operational changes (e.g., more frequent operational changes, potentially increasing the likelihood of equipment breakdown) versus a lower-ranked solution requiring less work from workers or fewer operational changes. In this regard, in one or some embodiments, the engineer may be presented with an array of potential solutions (selected by the algorithm based on factor(s)), and may select the optimal solution (selected by the engineer based on the factor(s) used by the algorithm and/or other factors not used by the algorithm). In the example presented above, in viewing the presented higher-ranked and lower-ranked solutions, the engineer may select the lower-ranked solution due to incremental oil uplift in the higher-ranked solution not justifying the additional work from the workers in the higher-ranked solution. In this way, the algorithm may present a set of “best” potential solutions that may assist engineers in making operational decisions.

As discussed above, selection of one or more design parameters using the analytical model and the optimization model are contemplated in one or more stages. By way of example, during the design stage, values for any one, any combination, or all of the following may be selected: (1) the number of wells for drilling; (2) the spacing between the wells drilled; (3) the well design parameters (e.g., vertical portion of the well, horizontal portion of the well; etc.); (4) the specifics of completions (e.g., the design of the hydraulic fractures); (5) well surveys (e.g., well surveys may define the trajectory of a well in 3 dimensions, and may comprise an array of numbers with 3 columns for x, y and z coordinates; by way of numerical example, the well survey may indicate that the well is vertical at a given co-ordinate on the map (x, y) indicate from z=0 to z=8000 ft, then the well turns horizontal over z=8000 ft to z=9000 ft, and then it is drilled horizontally over 10,000 ft, so it might say at z=9000 ft, x changes from 0 to 10,000 ft); (6) the hardware for the field (e.g., the width of the tubing; the width of the annulus; the size and number of compressor(s); the compression/pumping capacity of the compressor(s) for injection of gas into the tubing and/or the annulus); or (7) injected gas volume requirements. During the primary depletion stage, values for one or both of the following may be selected: (1) when to end the primary depletion stage (and to enter the huffing and puffing stage, such as when to begin cycle 1 as depicted in FIG. 10 ); or (2) optimizing production valve/choke setting to meet system constraints such as pipeline capacity or facility constraints (e.g., choke may comprise the cross-section of the pipe open to flow at the wellhead; the choke setting may control the choke to assist in regulating the flow from a respective well).

Generally speaking, during the gas injection stage, values relating to gas injection via tubing (e.g., huffing) and/or values relating to gas injection via the annulus (e.g., artificial lift) may be selected. More specifically, with regard to huff and puff in which gas is injected via tubing of injector wells, values may be selected for any one, any combination, or all of the following: (A) values selected for overall operation of huff and puff across multiple cycles; or (B) values selected for operation within a specific huff and puff cycle including values for operation of the injector well(s) and/or values for operation of the offset well(s).

With regard to (A), which is overall operation of huff and puff across multiple cycles, values may be selected for any one, any combination, or all of: (i) the number of cycles of huffing-and-puffing (such as three as illustrated in FIGS. 10-12 ); (ii) the timing of the cycles (e.g., how long to perform each cycle, wherein in one embodiment the length of each cycle being identical and alternatively, the length of each cycle varying); or (iii) the type(s) and/or characteristics of the fluid injected (e.g., the gas volume characteristics; the type of fluid such as separator gas, hydrocarbon gas, hydrocarbon liquid, water, CO₂, surfactant solutions, foams, etc.). As discussed further below, the values recommended or automatically selected for the overall operation of huff and puff across multiple cycles may be based on any one, any combination, or all of: performance in previous cycles; current field response; or oil/gas prices.

With regard to (B) as to operation of the injector wells, values may be selected for any one, any combination, or all of: (i) the specifics of the huffing in a respective cycle (e.g., the number of wells to select as injector wells; the specific wells to select as injector well(s) for injection of the gas into the tubing of a respective well selected as an injector; the sequence of which wells to select for injection); (ii) the injection rate of the gas into the tubing and/or the injection rate of the gas into the annulus; (iii) the injection volume of the gas into the tubing (e.g., the entire volume of gas injected over a single huffing cycle) and/or the injection volume of the gas into the annulus; (iv) the rate of injection over time during huffing and/or during artificial lift (e.g., step-change from zero rate of injection to the predetermined maximum rate of injection during huffing; ramping upward at a predetermined rate of change from zero rate of injection to the predetermined maximum rate of injection during huffing; other combinations of time and rate to modify rate of injection); (v) the duration of injection during huffing and/or during artificial lift; (vi) the sequence of which injector wells to inject gas in (e.g., injection starting time and/or injection duration); (vii) the sequence of which injector wells are artificially lifted; (viii) injection rates during huffing and/or during artificial lift; (ix) injection/producing configuration (e.g., average pressure of the area in which EOR occurs); (x) the type of gas for injection during huffing and/or during artificial lift; (xi) choke settings during artificial lift; (xii) whether to artificially lift an injector well (e.g., which wells to flow only naturally and which wells to artificially lift), and if so, the rate and duration of artificial lift; (xiii) whether to use the same type of gas for injection into the tubing (e.g., huff) and for injection into the annulus (e.g., artificial lift); or (xiv) if the same type of gas is used for injecting gas into the tubing (e.g., huff) and for artificial lift, determining how to split the gas between the two processes to maximize profitability of the operation.

With regard to (B) as to operation of the offset wells, values may be selected for any one, any combination, or all of: (i) which offset wells to cap and which not to cap (so that the offset well can continue producing); (ii) for producing offset well(s), determine whether/when to artificially lift (and for how long) or to flow naturally (e.g., based on injecting gas in an injector well, determine whether and/or when to artificially lift relative to the huffing of injecting gas in the injector well); or (iii) timing for artificial lift in offset well.

In particular, for the offset wells, the model(s) may determine (i) the offset wells selected for plugging during huffing; (ii) for the offset wells selected for plugging during huffing, how long to plug those offset wells (e.g., coextensive with the huffing; not coextensive with the huffing; same length of time to plug as the length of time for huffing into the injector wells; different length of time to plug than the length of time for huffing into the injector wells); (iii) which offset wells only to flow naturally versus using artificial lift; (iv) for offset wells with artificial lift, the injection volume of the gas into the annulus; (v) the rate of injection over time during artificial lift (e.g., step-change from zero rate of injection to the predetermined maximum rate of injection during huffing; ramping upward at a predetermined rate of change from zero rate of injection to the predetermined maximum rate of injection during huffing; other combinations of time and rate to modify rate of injection); (vi) the rate and/or the duration of injection during artificial lift; (vii) the sequence of which offset wells are artificially lifted; (viii) injection rates during artificial lift; (ix) injection/producing configuration (e.g., average pressure of the area in which EOR occurs); (x) the type of gas for injection during artificial lift; or (xi) choke settings during artificial lift.

Thus, the design and operational mechanism may be configured to support decisions in one or more stages of hydrocarbon extraction even in the presence of subsurface (both geologic and fluid system) and market uncertainties. Such an integrated system may improve or optimize reservoir/field management under any desirable operational and environmental constraints.

Further, given additional information, such as additional data in the course of performing EOR in the field, the analytical model may be updated. For example, responsive to receiving additional diagnostic data, the analytical model may be updated, such as illustrated in FIG. 10 in which model calibration may be performed during the primary depletion stage and in one or more of the cycles of the huff and puff stage. By way of example, various parts of the model, such as any one, any combination, or all of the following may be updated: parameters; vias, or time lag.

Further, the present methodology is scalable, in terms of number of wells and/or geometric configurations of wells. As such, new wells may be added, or old wells may be removed. In addition, well-to-well communication may be tuned based on distance, number of neighbors, and level of communication as a function of stress direction in the subsurface. As such, the methodology may be applied to a variety of contexts, whether on a pad-scale or on a commercial-scale. In this way, the methodology may be applied to a large number of wells (e.g., greater than wells) across a single interval (or other zone of interest) or across multiple reservoir intervals (such as one or more intervals) and thus may assist in the design of a pilot-scale project and/or a full-field scale application.

Thus, the methodology may be configured to predict one or more EOR metrics within the field, such as within the one or more injector well(s) and/or within the one or more offset wells. Merely by way of example, the methodology may predict how bottomhole pressure BHP is expected to build in an injector well as a function of any one, any combination, or all of: well-to-well connectivity (e.g., an interwell connectivity metric); a number of wells; or configuration of neighboring wells. Further, the methodology may predict the metric in one or more offset wells. For example, the methodology may predict how BHP may build in offset wells as a function of injection from neighboring wells. The methodology may further predict one or more metrics outside of the field (e.g., predicting what fraction of injectant will leak outside the well pattern).

In addition, the methodology may be configured to predict the complex interactions between the one or more injector well(s) and the one or more offset wells. For example, the methodology may determine how much compression (or how much injection rate) may be needed to overwhelm well-to-well communication (e.g., to overwhelm the loss of fluids to other wells) before the pressure of the injector well(s) and the offset wells may increase. Thus, in one or some embodiments, the methodology may determine the compression necessary to overwhelm well-to-well communication as a function of any one, any combination, or all of: pressure; fluid properties; or one or more aspects of the wells (e.g., layout or geometry) of the wells). In this regard, the compression necessary may be a function of aspects that are controllable (e.g., one or both of the pressure applied, the fluids selected, etc.) and other aspects that may not be controllable (e.g., in an existing field of wells, the well layout, pattern, or spacing).

In this regard, the methodology may generally assist in hydrocarbon management. For example, the analytical model, as part of the methodology, may assist in determining any one, any combination, or all of: a duration of injection (such as the number of injection days) for a given well configuration, communication and compression/pumping in order to reach a target pressure during injection; which wells to pick as injectors; how to split the injected fluids among many wells to maximize a pressure metric (such as average pressure) over an area of interest (e.g., over one or more intervals); and selection of strategies to contain the transport of injected fluid on injection rates, pressure builds and leak outside the area of interest (e.g., plug off one or more leak zones, such as by intentionally injecting cement or polymers to plug off the one or more leak zones; conformance control in terms of attempting to direct the fluid in a certain direction: injecting water which is immiscible thereby creating a larger resistance for transport). Merely as one example, the optimization algorithm may analyze whether and how to split injected fluids amongst multiple injector wells. In one or some embodiments, the optimization algorithm may analyze one or more metrics, such as a pressure metric. In particular, the optimization algorithm analyzes the split of injected fluids in order to a maximum pressure needed in the one or more injector wells. In response, the determined maximum pressure may then be used in order to select the hardware, such as the compressor, needed to generate such maximum pressure and the costs associated with purchasing such hardware. In this way, the optimization algorithm may assist in determining the various operational conditions warranted (e.g., the maximum pressure) and in selecting the appropriate hardware capable of performing under the operational conditions (e.g., purchasing the smallest compressor that still is capable of generating the maximum pressure). In this regard, the methodology may be used in a predictive mode and/or in an improvement/optimization mode in the field given certain constraints.

Referring to the figures, FIG. 1A illustrates a schematic 100 of the analytical model for a 3-well system with an injector well (well #1 (110)), surrounded by two offset producer wells (well #2 (120); well #3 (130)). In practice, fluid is injected from a compressor/pump into well #1 (110) thereby creating bottomhole pressure P1 in well #1 and bottomhole pressure P2 in well #2 (120) and bottomhole pressure P3 in well #3 (130). In turn, the fluid travels to offset wells, including well #2 (120) as shown by q₁₂, and to well #3 (130) as shown by q₁₃. The fluid further may leak outside the area of interest as shown in q₁. Arrows 140, 142, 144, 146 in FIG. 1A are indicative of the amount of fluid injection with arrow 140 into well #1 being the biggest arrow and the most injection. In the event that arrow 142 associated with q₁₂ or arrow 144 associated with q₁₃ is large, more fluid (as indicated by arrow 140) would need to be injected to build pressure in the system.

As discussed in more detail below, the analytical model is configured to predict one or more EOR subsurface responses, such as bottomhole pressure (P1) of the injector well and bottomhole pressure (P2, P3, etc.) in one or more offset wells during EOR processes.

FIG. 1B is a top view 150 of twelve horizontal hydraulically fractured wells in an interval 152 showing fluid transport from the injection wells, including, for example, well #16 for days followed by well #14 for 30 days, to its neighboring wells based on stress orientation within the subsurface. FIG. 1B is depicted merely for illustration purposes. Different numbers of wells, different layouts, and different numbers of intervals (e.g., whether a single interval or multiple reservoir intervals) are contemplated.

The wells depicted in FIG. 1B are existing wells, which have already been subject to hydrocarbon extraction. In particular, these wells have already been subject to fracturing, with the wells previously having produced hydrocarbon and were depleted or are nearly depleted in the primary depletion stage, discussed further below. In one embodiment, the methodology seeks to extract more hydrocarbon from these presumed depleted wells by injecting fluid (e.g., water and/or gas) in order to energize the system (e.g., build pressure close to the existing wellbore/fractures) for swelling and reducing fluid viscosity, thereby energizing the system locally and then producing hydrocarbons back from the same wellbore. Further, as discussed above, the analytical model may be used to determine the number of wells, the placement of the wells, the configuration of the wells, the fracturing associated with the wells, etc. during the design stage.

In this regard, production data for these wells are available, and may therefore be used by the analytical model in order to predict the effect in the subsurface when liquid/gas are injected, such as in gas injection through tubing of a respective injector well. In this regard, the analytical model, using the available production data and generally accepted geomechanical principles) may predict, for a given well at a given pressure, the expectation as to the flow of the liquid/gas from an injector well to one or more offset wells (e.g., how the connectivity, such as fluid connectivity, between the wells may change as a function of pressure). Specifically, the analytical model may consider any one, some or each of the following three different domains: (1) the geomechanics of the system (e.g., how the fractures from adjacent/different wells may communicate with each other); (2) the physical location of the wells; and (3) the chemistry or fluid mechanics involved (e.g., the quantity of fluid/gas to be added to build sufficient pressure and the effectiveness to build pressure in order to create an enhanced/upload for a fluid flow back from the well).

In one or some embodiments, the analytical model may be based on subdividing the interval into discrete units, and generating an indicator of the fluid interconnectivity within the discrete unit. In a specific embodiment, the interval may be subdivided by wells, such as pairs of wells. In turn, an interwell connectivity metric may be assigned to respective pairs of wells indicative of the fluid interconnectivity amongst the respective pair of wells. It is noted that the interwell connectivity metric need not be limited to only two wells in a pair. Greater than two wells may be assigned an interwell connectivity metric. Thus, the interwell connectivity metric may be an indicator of physical proximity of the plurality of wells and/or subsurface indicators (e.g., stress orientation in the subsurface). For example, a given injector well and its immediate physically adjacent neighbor well may have a higher interwell connectivity metric than a secondary well (or even tertiary wells) that is not the given injector well's immediate neighbor (e.g., once removed or twice removed from the given injector well). Though, the secondary well or the tertiary well may still have some connectivity with the given injector well (as indicated by the interwell connectivity metric). However, physical proximity is merely one aspect accounted for with regard to the interwell connectivity metric. Rather, the interwell connectivity metric may account for other more complex subsurface features, such as stress orientation. In this way, the interwell connectivity metric may depend on physical proximity of the wells as well as direction of stressors in the subsurface reservoir.

Referring back to FIG. 1B, the interval 152 may be viewed as a matrix with one, some, or all pairs of adjacent wells being assigned an interwell connectivity metric (F_(ij)). For example, based on prior subsurface data, the analytical model may determine an expected fluid connectivity in the subsurface responsive to injection of fluid within one of the wells (e.g., injection of gas into tubing of an injector well, see FIG. 13A). In the particular example illustrated in FIG. 1B, the analytical model may identify the stress state of the geomechanics of the system and determine that injection in well #16 results in an expected effect on well #15, well #29, and well #5 (but not well #3 or well #4, even though physically adjacent). In this way, the analytical model may identify the stress field in such a way as to define adjacency from a fluid flow perspective. Given this, injector well #16 is connected, from a fluid perspective, with well #15, well #29, and well #5 (e.g., injecting fluid into well #16 results in fluid flow to well #15, well #29, and well #5 but not to well #3 or well #4).

As such, the analytical model may assign the interwell connectivity metrics to the following pairs: well #16:well #15 (identified as F_(16,15)); well #16:well #29 (identified as F_(16,29)); and well #16:well #5 (identified as F_(16,5)). In this way, the analytical model may be tailored to any interval with any layout of wells.

FIG. 1B illustrates a top view 150 of a 2-D configuration in which there are 2 rows of wells in the same plane and the same depth in the earth. Alternatively, the analytical model may consider a 1-D configuration (e.g., wells, 13, 14, 15, 16, 29, 6). Still alternatively, the analytical model may consider a 3-D configuration with wells at different depths (e.g., one or more wells in one horizontal plane in the earth and other wells in another horizontal plane in the earth).

FIG. 1C illustrates a 3-D configuration 180 illustrating injection in well B1, in a 3D setting with 2 reservoir intervals A and B showing propagation of injected gas (shown by arrows 182, 184, 186, 188 to well A1, well A2, well A3, and well B2, respectively, and arrow 190 to another part of reservoir interval B) and associated pressure perturbation along wells in the same reservoir interval (e.g., reservoir interval B) and also in other reservoir interval(s) (e.g., reservoir interval A).

FIG. 2A is a block diagram of the analytical model 200. As discussed above, the analytical model 200 may include one or more inputs and one or more outputs. As shown in FIG. 2A, the inputs include one or more injection rates, one or more types of fluid for injection, and one or more parameters (such as a and b, discussed below). The output for the analytical model 200 includes one or more indicators of the subsurface responses.

In this way, the analytical model 200 may be configured to predict one or more aspects of the reservoir, such as reservoir pressure and/or other subsurface response factors. In particular, the analytical model 200 may predict one or more subsurface responses (e.g., the bottomhole pressure in each well) respond to one or more stimuli such as fluid injection, duration of the injection operation, the sequence of the injection, and/or average pressure of the area in which EOR occurs. The analytical model 200 may incorporate anisotropic stress condition in the subsurface and resulting anisotropy in gas transport to provide a geologically representative prediction of the pressure build. Further, as discussed above, the analytical model 200 may consider a wide range of injected fluids (as illustrated by the input for one or more types of fluids), including any one, any combination, or all of: separator gas; hydrocarbon gas; hydrocarbon liquid; water; CO₂; surfactant solutions; or foams.

In one or some embodiments, the analytical model 200 may be manifested in one of several ways. In one way, the analytical model may comprise one or more equations, such as the following:

$\begin{matrix} {{V_{1}\frac{dP_{1}}{dt}} = {P_{1}\left( {q_{inj} - {\sum q}} \right)}} & (1) \end{matrix}$ $\begin{matrix} {{V_{2}\frac{dP_{2}}{dt}} = {{P_{1}q_{12}} - {P_{2}q_{2}}}} & (2) \end{matrix}$ $\begin{matrix} {{V_{3}\frac{dP_{3}}{dt}} = {{P_{1}q_{13}} - {P_{3}q_{3}}}} & (3) \end{matrix}$

with V₁, V₂, and V₃ comprising control volumes represent parameters whose values that may be estimated based on primary depletion. As discussed below, additional or different terms may be used in the equations comprising the model. For example, it is noted that the system may further consider variable(s) directed to the physics (e.g., δ). In such an instance, Equations (1)-(3) may be updated as follows:

$\begin{matrix} {{V\frac{dP}{dt}} = {{P_{1}\left( {q_{inj} - {\sum q}} \right)} + \delta}} & (4) \end{matrix}$ $\begin{matrix} {{{V_{1}(t)}\frac{{dP}_{1}(t)}{dt}} = {{P_{1}\left( {{q_{inj}\left( {t - \tau} \right)} - {\sum{q(t)}}} \right)} + {\delta_{1}\left( {t,q,P} \right)}}} & (5) \end{matrix}$ $\begin{matrix} {{{V_{2}(t)}\frac{{dP}_{2}(t)}{dt}} = {{{P_{1}(t)}{q_{12}(t)}} - {{P_{2}(t)}{q_{2}(t)}} + {\delta_{2}\left( {t,q,P} \right)}}} & (6) \end{matrix}$ $\begin{matrix} {{{V_{3}(t)}\frac{{dP}_{3}(t)}{dt}} = {{{P_{1}(t)}{q_{13}(t)}} - {{P_{3}(t)}{q_{3}(t)}} + {\delta_{3}\left( {t,q,P} \right)}}} & (7) \end{matrix}$ $\begin{matrix} {{q(t)} = {F_{cd}\frac{\Delta{P(t)}}{\mu}}} & (8) \end{matrix}$ $\begin{matrix} {F_{cd} = {ae^{b\overset{¯}{P}}}} & (9) \end{matrix}$ $\begin{matrix} {{P(0)} = P_{0}} & (10) \end{matrix}$

-   -   ΔP representing the pressure difference between the two wells;     -   μ representing viscosity of the injected fluid;     -   a and b relate the conductivity of well-to-well conduit to the         average pressure (P_(avg)) within the well pattern with a         comprising an empirically determined constant and b represents a         compliance parameter indicative of lag factor;     -   q represents fluid transport between two wells with ΔP being the         pressure differential between the two wells;     -   q_(inj) represents the gas injection rate; and     -   F_(cd) comprises, in one or some embodiments, the interwell         connectivity metric (with cd in subscript representing         fracturing conductivity), such as an indicator of the fluid         transport between wells. F_(cd) may be indicative of the width         of the fractures for the respective wells and the ability for         fluid transport between the wells. In this regard, F_(cd) may be         indicative of one or both of connectivity or fluid transport         (which may comprise a multiphase flow component). Other         interwell connectivity metrics are contemplated. In practice,         each pair of wells may have an assigned F_(cd), including well         #16:well #29 (represented by F_(16,29)); #16:well #5; etc. As         shown, F_(cd) may be represented mathematically as dependent on         parameters “a” and “b” that relate the conductivity of         well-to-well conduit and to the average pressure (P_(avg))         between two wells. It is noted that the analytical model 200 may         account for different fluids injected (see, e.g., μ which         represents the viscosity of the fluid).

As discussed further below, δ may be determined by machine learning. Merely by way of example, data may be used in order to update the analytical model (see model calibration 1010, 1012, 1014, 1016), as discussed further below.

In this way, the analytical model may comprise a series of differential equations that represent mass balance on a control volume probed by injected fluid around each well, such as schematically illustrated in FIG. 1A for a system comprising (or consisting of) 3 wells or illustrated in FIG. 1B for a system comprising (or consisting of) 12 wells. The analytical model 200 may manifest the differential equations in one of several ways. In one embodiment, the analytical model may comprise a Bayesian probabilistic framework for differential equation models that partially or fully explores the uncertainty space for uncertainty quantification and model parameter estimation. In practice the equations may be coded in a variety of ways, such as via a Microsoft Excel spreadsheet or in Python, which may be used by Reservoir Engineers to match field production and run sensitivity studies.

As discussed above, the analytical model 200, for the layout illustrated in FIG. 1A, may predict the bottomhole pressure in the injector well (P₁) as well as the two offset wells (P₂, P₃).

Further, the analytical model 200 may be updated periodically, such as based on receipt of diagnostic data, as discussed above. See FIGS. 10-12 . Various types of diagnostic data are contemplated, including any one, any combination, or all of: bottomhole pressure (e.g., pressure measurements in the wellbore); compositional samples collected from the well (e.g., fluid samples collected and analyzed to determine the chemical signature of the fluid samples); or (3) production data (e.g., ratios of the different fluids, such as gas to oil, oil to water, gas to water, and trends of the changes in the different fluids). For example, as more and more injection data are collected, the analytical model 200 may learn appropriate values of the volumes (e.g., V₁, V₂, and V₃), and one or more of the parameters (e.g., a and b) may be updated. The analytical model 200 may estimate the amount of fluid transported from the injector well to each of the offset wells (q₁₂ and q₁₃) as a function of pressure difference between the two wells (ΔP) and viscosity of the injected fluid (μ). The analytical model 200 may also predict the amount of fluid lost from each of the wells to its depleted surrounding (q₁, q₂, and q₃). In this way, the analytical model 200 may provide an acceptable match to pressure builds for the injector well and offset well(s) in a gas injection based EOR field trial. In one or some embodiments, once the analytical model 200 predictions are validated using these field data, the analytical model 200 may be used to predict pressure response in the future.

Referring back to FIG. 1B, in the illustrated scenario, all of the twelve wells are in the same reservoir interval 152 and fluid is injected in well #16 (with well #16 designated as (i) for injection) and thereafter in well #14. Injecting into well #16 results in part of the injected fluid being transported towards neighboring wells (well #15 as illustrated by arrow 160, well #29 as illustrated by arrow 162, well #5 as illustrated by arrow 164), and subsequently to nearby wells (such as well #18, well #4 etc.). In addition to connectivity with offset wells to the right of well #16 (well #29) and to the left of well #16 (well 15), the analytical model may incorporate a connectivity in the upper-right and/or lower-left direction based on the stress anisotropy in the subsurface. Further, injecting into well #14 results in part of the injected fluid transports towards neighboring wells (well #13 as illustrated by arrow 166, well #15 as illustrated by arrow 168, well #2 as illustrated by arrow 170), and subsequently to nearby wells. Similar to the 3-well scenario illustrated in FIG. 1A, the analytical model is configured to predict bottomhole pressure (BHP) in the injector well (#16) and all the offset wells, as shown in graphs 300, 350 in FIGS. 3A and 3B, respectively of the BHP over time for the different wells (e.g., well 1H (310); well 2H (312); well 3H (314); well 4H (316); well 5H (318); well 18H (320); well 13H (360); well 14H (362); well (364); well 16H (366); well 29H (368); well 6H (370)). The analytical model 200 may also be configured to predict the amount of fluid flowing between each neighboring well pairs. Alternatively, or in addition, the analytical model 200 may predict the amount of injectant lost over time (e.g., cumulative loss) and/or instantaneous loss outside the region marked in FIG. 1B, as shown in the graph 400 in FIG. 4 illustrating cumulative gas lost 410 and instantaneous gas lost 420.

FIG. 2B is a block diagram of the design and operational mechanism 250, including potential system design parameter(s) values 260, set(s) of system parameter values for analysis 270, analytical model 200 of FIG. 2A, and design parameter selector 280.

As discussed above, the analytical model may be used in a variety of contexts, including in designing a pilot-scale project or a full-field scale application. In this regard, the analytical model may be used in a predictive mode or in an improvement/optimization mode using design and operational mechanism 250 in order to determine, given certain constraints, the parameters to select. This is illustrated, for example, in FIGS. 9A-C. As discussed above, the design and operational mechanism 250 may be used in one or more stages of hydrocarbon extraction, such as any one, any combination, or all of: the design stage; the primary depletion stage; or the gas injection stage.

In particular, in a first step, values (such as a range of values) of input parameters may be determined, such as reflected in potential system design parameter(s) values 260. As discussed above, in the gas injection stage, input parameters may include: the choice of wells (including which well(s) for injection and/or which wells not for injection); how much fluid to inject; sequence of fluid injection (e.g., in the example illustrated in FIG. 1B, one sequence comprises well #16, then well #4 and then well #3); duration of injection (e.g., in the example illustrated in FIG. 1B, inject for 30 days into wells #4 and #16, and then inject for 15 days only in well #16); etc. Alternatively, or in addition, design and operational mechanism 250 may be used to select design parameter(s) in the design stage (e.g., the number of wells, the spacing of wells, the design of the wells, the hardware (e.g., the compressor and/or piping)) and/or in the primary depletion stage (e.g., the timing when to end primary depletion).

Practically speaking, there may be physical constraints and economic constraints in the values. For example, physical constraints may be imposed by a real system. In particular, the real system may only have a given amount of gas available and/or a certain amount of pressure available without a resulting safety issue. In this regard, the physical constraints may dictate bounds as to potential values for the input parameters. As another example, economic constraints may likewise limit the potential values for the input parameters. For example, cost limits may dictate a cap on the amount of spend, with the potential spend varying at different stages (e.g., a budget limit of $1 million until receiving positive feedback, after which the budget limit increases to $10 million in order to purchase additional equipment (e.g., purchasing a larger compressor) or performing additional acts (e.g., injecting in more wells)).

In a second step, various given sets of values for the input parameters (reflected in set(s) of system parameter values for analysis 270) may be analyzed using the analytical model 200 in order to determine improved or optimal values for the input parameters based on pre-defined objectives or metrics. In one or some embodiments, the design and operational mechanism 250 may be configured to handle one, some or each of continuous (such as injection rates in the gas injection stage), discrete (such as number of wells and well configuration in the design stage) or categorical (such as a compressor selected from a set of commercially-available compressors) decisions. The design and operational mechanism 250 may use one or multiple optimization approaches based on the availability of model sensitivity (e.g., adjoint). In one or some embodiments, the design and operational mechanism 250 may include one or more optimization models, which may be manifested in one of several ways, such as in equation form.

$\begin{matrix} {\max{J\left( {P,q,r} \right)}} & (11) \end{matrix}$ $\begin{matrix} {{V\frac{dP}{dt}} = {g\left( {P,q} \right)}} & (12) \end{matrix}$

where J(P, q, r) is the objective function that represents user-defined physical or economic metric to be optimized. Further, P may comprise the pressure in the subsurface, q may comprise flow rates, r may comprise a discount rate (e.g., assuming that J is indicative of net present value). As discussed in more detail below, when seeking to optimize for an identified metric, the optimization may focus on net present value or another defined value. For example, the object function may include any one, any combination, or all of: the cost of the gas; cost of drilling/completion; cost of treating the gas after its production; or the value of the oil.

For example, the values for the input parameters may be varied in a systematic manner in to identify an improved or a “best solution,” based on the pre-defined objectives or metrics. An initial set of system parameter values for analysis may be selected in one of several ways, such as based on the engineer's judgement. After analysis of the initial set of system parameter values, the design and operational mechanism 250 may systematically alter the values of the system parameters through the design space in order to select, by the design parameter selector 280, an improved or optimal solution for the set of system parameter values. In this way, the design and operational mechanism 250 may iterate to progress to the selected solution.

Referring back to the example illustrated in FIG. 1B, the design and operational mechanism 250 may begin by analyzing an initial set of parameter values (automatically generated and/or engineer generated). In one or some embodiments, for the gas injection stage, each of the 16 wells may be analyzed as an injector well. Alternatively, certain wells, such as those at the corners of the boundary as identified at 152, may be excluded due to some of the gas moving outside of 152 (e.g., wells #1, 6, 13, and 18 are excluded). In contrast, one or more wells (such as combinations of wells) further away from the corners of the boundary as identified at 152 (e.g., wells #3, 4, 15, and 16) may be examined to determine the combinations of the wells, the rate of injection, and the duration of injection will yield the best results. As discussed above, the analysis for various aspects, including BHP (see FIGS. 3A-B), fluid leaking out of the area of interest (FIG. 4 ), and oil uplift (see FIGS. 5A-B). In particular, FIG. 5A is a graph 500 of oil production rates (barrels/day) over time for wells #1 (510), #2 (512), #3 (514), #4 (516), #5 (518), and #18 (520). FIG. 5B is a graph 550 of oil production rates (barrels/day) over time for wells #13 (560), #14 (562), #15 (564), #16 (566), #29 (568), and #6 (570).

FIG. 6 is a schematic 600 indicating instantaneous bottomhole pressure response in the injector well (P₁) and delayed pressure response in an offset well (P₂) due to change in injection rate in the injector well (P₁). As discussed above, in one or some embodiments, the analytical methodology may be based on analysis of a metric, such as pressure, in the various wells. In a specific embodiment, the analytical methodology may be based on the time lag (Δt) between a change in injection rate at a given injection well (e.g., well 1 (110) in FIG. 1A) and when the bottomhole pressure in an offset well (e.g., well 2 (120) in FIG. 1A) responds to the change. In such a methodology, any one, any combination, or all may occur: (1) interwell connectivity (F) may be described by using hydraulic diffusivity between wells; (2) the variation in interwell conductivity (F) may be parameterized by a function, such as an exponential function, with a coefficient and exponent fit to experimental data measured from the system (e.g., see Eq. (5) above); or (3) using the interwell connectivity (F) from an exponential fit to field data, various aspects of the wells may be obtained (e.g., an estimate of the fracture width (w) of the conduit connecting the two wells may be obtained)

Referring back to FIG. 6 , schematic 600 illustrates the time lag (Δt) at two different instances, when injection rate (e.g., in which gas is injected into a tubing of an injector well) is decreased from q_(a) to q_(b) (e.g., a draw-down) resulting in Δt₁ and when the injection rate is increased from q_(b) to q_(c) (e.g., a build-up) resulting in Δt₂. Thus, q_(a), q_(b), and q_(c), representing three different injection rates, enable identifying effects of the rate changes. Specifically, the rate changes may make opportunistic use of field offsets when there is a change in compressional pumping rate, tracking when an event (e.g., the pressure change) occurs at one well (e.g., in an injector well) and when that event is felt at an offset well (e.g., detects the lag), with the effect on the offset well being converted or transformed into an interwell connectivity. This type of data (e.g., monitoring changes in pressure) is typically already being collected, which may then be mapped by interwell connectivity as a function of pressure. As discussed below in FIG. 7 , there are 2 evident trends: (1) drawdown with subscripts d (when the pressure is decreasing); and (2) buildup with subscripts b (when the pressure is increasing).

In one or some embodiments, using the distance between the wellbores (

), width of the fracture conduit (w), porosity of the fracture (ϕ), viscosity of the fluid (μ), and total compressibility of the system (c_(t)), interwell conductivity may be calculated using the hydraulic diffusivity equation:

$\begin{matrix} {F = {\phi\mu c_{t}{{w\left( \frac{\ell^{2}}{\Delta t} \right)}.}}} & (13) \end{matrix}$

As discussed above, Eq. (13) may be coded in a Microsoft Excel Spreadsheet or in Python, which may allow engineers to use the tool in a variety of contexts, such as in any one, any combination, or all of: for a wide range of pressures; for various numbers of wells; and for various types of fluid and rock properties. For example, responsive to determining the interwell connectivity (F), the effective width of the fracture conduit (w) may also be estimated from Eq. (13), if all other geometry parameters and fluid properties are known.

FIG. 7 is a graph 700 of interwell conductivity (F) versus average bottomhole pressure (P avg) for buildup and drawdown in which the interpreted well-to-well connectivity (computed from the time lag for pressure response) is plotted against the average bottomhole pressure during both drawdown and buildup. In particular, the graph 700 in FIG. 7 illustrates the loss of injection rate (drawdown) 710 along curve 714 in a direction indicated by arrow 712. Further, the graph 700 in FIG. 7 illustrates the increase in injection rate (buildup) 720 along curve 724 in a direction indicated by arrow 722.

As shown in FIG. 7 , the interwell connectivity may monotonically increase with increasing average pressure. In particular, when injection rate into a respective injector well increases (e.g., from q_(b) to q_(c) as illustrated in FIG. 6 ), the bottomhole pressures increases, and the event may be regarded as a buildup event. In contrast, when injection rate declines in the respective injector well (e.g., from q_(a) to q_(b) as illustrated in FIG. 6 ), bottomhole pressure decreases, and the event is regarded as drawdown. In the case illustrated in FIG. 7 , 5 buildup events and 6 drawdown events are analyzed between the injector well (e.g., Well 1 (110) in FIG. 1A) and an offset well (e.g., Well 2 (120) in FIG. 1A). As discussed above, interwell connectivity, which may be inferred from the analysis, may be parameterized in terms of a constant “a” and an exponent “b”, which multiplies the average bottomhole pressure of the system. As shown in FIG. 7 , two distinct trends appear for interpreted interwell connectivity during drawdown and buildup. The curvature of the drawdown curve (b_(d)) is larger than the curvature of the buildup curve (b_(b)), which indicates that the conductivity is more sensitive to change in average pressure during drawdown compared to buildup.

The methodology may be extended to quantify response times and conductivity between the injector well and the other offset well (e.g., well 3 (130) in FIG. 1A). It may likewise be extended to any number of total wells with any number of injectors. Further, as discussed above, the methodology may be applicable to a wide range of injected fluids including any one, any combination, or all of: separator gas; hydrocarbon gas; hydrocarbon liquid; water; CO₂; surfactant solutions; foams, etc.

In one or some embodiments, the methodology may be used for fracture characterization. For example, fluid injection may be used as a fracture diagnostics technique to quantify well connectivity as a function of pressure. In one or some embodiments, the fracture diagnostics technique may indicate one or more aspects of the fracture, such as the exact location of the fracture. In turn, the fracture characterization may assist in the design of fracturing/completion on other wells (e.g., other wells in the vicinity) and/or assist in improving/optimizing well spacing and stacking (e.g., vertical and lateral spacing) in the development of unconventional reservoirs. Merely by way of example, the fracture characterization may assist in selecting any one, any combination, or all of the following aspects of fracturing/completion: type of proppant; amount of proppant; number of clusters/stage; stage spacing; amount of fluid used for completion; or type of fluid used for completion. Thus, in practice, the fracture characterization may be used to select or modify one or more aspects of the fracturing/completion of the other wells.

FIGS. 8A-C illustrate top views of three different scenarios 800, 820, 840 for distribution of hydraulic fractures for two horizontal wells. Specifically, FIG. 8A illustrates hydraulic fractures in well 1 (802) with fractures 806 and in well 2 (804) with fractures 808, in which the fractures 806, 808 do not hit each other. FIG. 8B illustrates hydraulic fractures in well 1 (822) with fractures 826 and in well 2 (824) with fractures 828, in which the fractures 826, 828 do hit each other. FIG. 8C illustrates hydraulic fractures in well 1 (842) with fractures 846 and in well 2 (844) with fractures 848, and further with fractures 850 that cross both well 1 (842) and well 2 (844), in which the fractures 846, 848 are zippered and fractures 850 are intermingled. Thus, in one or some embodiments, responsive to determining that the time lag (Δt) is at or nearly zero, it may be determined that the fractures comprise fractures 850, which cross multiple wells. Conversely, responsive to determining that the time lag (Δt) is greater than a predetermined amount, it may be determined that the fractures do not comprise fractures 850.

Based on the time lag (Δt) between a change in injection rate at a well (e.g., well 1), and the sensed change in the bottomhole pressure in an offset well (e.g., well 2), the fractures may be characterized at least in part. For example, based on the time lag (Δt), one of more of the fracture diagnostic scenarios may be eliminated. For example, (scenario C in this case) may be eliminated. Injection of gas or fluid in one more wells may be used as a fracture diagnostic technique to eliminate scenarios inconsistent with the interpreted interwell conductivity. Thus, in an instance where the injector well includes fractures and the offset well(s) likewise include fractures, injecting gas into the injector well and sensing the response in the offset well(s) may assist in characterizing the fractures, such as potentially eliminating fracture scenarios, and in turn narrowing the uncertainty in the subsurface.

Further, as discussed above, interwell connectivity may be strongly correlated of pressure whose behavior may be highly hysteretic. In addition, interwell connectivity may be approximately twice as sensitive to pressure compared to lab-derived pressure dependent permeability on intact rocks, which may indicate that the interwell connectivity may account for non-ideal situations (and the potential complexities of fractures in the subsurface) not considered in simulations.

Also, interwell connectivity during injection at high bottomhole pressure may diminish significantly once the wells are depleted. Consequently, wells may be more disconnected at low bottomhole pressure or during depletion compared to high pressure and injection. Thus, in one or some embodiments, the interwell connectivity may be monitored in order to determine when the well is depleted (e.g., as an indicator of well depletion). In this regard, the interwell connectivity may be used when to begin and/or when to end EOR. For example, the analytical model in combination with an improvement or optimization model may determine when to end the primary depletion stage (and begin the gas injection stage) based on the determination when the well(s) are depleted.

Finally, a calibrated model that describes interwell connectivity as a function of pressure may be used to estimate the amount of gas needed to build pressure as a function of injection rate.

The analytical approach thus allows the strength of well-to-well interaction to change as a function of the average bottomhole pressure and whether the pressure increases or decreases. This added versatility makes the analytical approach broadly applicable across well-to-well interactions characterized by multiple flow regimes. In this way, another variable in terms designing operations (e.g., controlling and selecting operations) may comprise whether to build-up or to draw down. Thus, the hysteretic behavior of the system may be used to design EOR operations.

Further, the analytical approach may be significantly faster to implement and run than a hydraulic fracturing simulation based approach, as discussed above. Because of its simplicity, the methodology may be automated. The methodology need not attempt to differentiate between various mechanisms behind the pressure dependence of the interwell conductivity. Rather, the methodology may lump some or all of the geomechanical complexity into one or more terms of Eq. (5), which 2 parameters “a” (a constant) and “b” (in an exponent). Additionally with regard to simplicity, the methodology may be based at least in part (or entirely) on the time lag (Δt) needed for a pressure signal to travel from an injector to an offset well. In this way, the methodology need not depend on the magnitude or percent pressure change in a given time interval.

Moreover, the methodology may be validated on well-to-well communication observed from an EOR field trial. In this manner, the exponential functional form is contemplated to be broadly applicable, though the specific parameters in the methodology (e.g., “a” and “b”) may be tuned for different systems.

As discussed above, the analytical model may be used in a variety of contexts. For example, the analytical model may be used in combination with another model to select parameters to improve or optimize one or more stages of hydrocarbon extraction, such as any one, any combination, or all of: the design stage; the primary depletion stage; or the gas injection stage. Further, it is noted that the stages, including the primary depletion stage and the gas injection stage, may span at least one decade, at least two decades, at least three decades, or more. As such, the efficiencies derived from use of the model(s) may significantly improve extraction of hydrocarbons.

In one or some embodiments, the system may be composed of multiple components, such as any one, any combination, or all of: wells; reservoir(s); surface pipelines; and equipment (e.g., compressor(s)). The analytical model may be configured to model one or more processes, such as the physical process (e.g., the fluid flow) and/or chemical processes (e.g., chemical reactions) of fluids in one, some or each of the system components. In one or some embodiments, the analytical model comprises a single model to model each of the processes, including the physical process and the chemical process. Alternatively, the analytical model comprises separate models to model each of the processes, including a physical process model and a chemical process model.

FIG. 9A is a block diagram 900 of a system model 910 that includes parts for an analytical model 912 and an optimization model 914, with the system model 910 being used in one or more stages of hydrocarbon management, including the design stage, the primary depletion stage, and the gas injection stage (e.g., one or more huff and puff stages). As discussed above, the analytical model 912 may be configured to generate a response in the subsurface, such as a fluid response in the subsurface to one or more stimuli, such as gas injection. The optimization model 914 may be configured to analyze, in combination with the analytical model, inputs of the potential values for parameters in the one or more stages of hydrocarbon management and generate outputs of the values selected. Alternatively, the analytical model 912 may be used to characterize a part of the subsurface (e.g., characterize hydraulic fractures in the subsurface, as discussed above). In this regard, the analytical model 912 may be used in one or more different contexts.

FIG. 9B is a block diagram 920 of the design model 930 for optimization during the design stage (an example of which is shown as design model 1020 in FIGS. 10-12 ). As discussed above, the analytical model 912 may comprise an interconnectivity model, such as reservoir interconnectivity model 932. Further, the optimization model 914 may be tailored to a specific stage of hydrocarbon management, such as the drilling+construction stage, and shown as drilling+construction optimization model 934.

In one or some embodiments, the design model 930 may include one or more constraints in selecting the optimal values for the design stage, with the constraints including any one, any combination, or all of: practical constraints (e.g., maximum rate of gas that can be delivered by a gas pipeline; contractual obligations to deliver a certain amount of gas to a specific customer; equipment malfunction that might limit injection rates/durations; weather events affecting electric power supply or operability (e.g., the winter storm in Texas in February 2021)); budgetary constraints (e.g., gas price; transportation cost charged by pipeline operators; limits on capital or operating costs set in annual budgets); or best practices/intuition (e.g., recommendation not to make significant changes on a Friday afternoon, as field operators may not be able to respond quickly if a problem arises).

In one or some embodiments, the constraints may be embedded in the math as either equations/inequalities (e.g., the production should be less than a first predetermined number or the budget should not increase beyond a second predetermined number) or rules (e.g., if “X” occurs, then “Y” should be performed). In one or some embodiments, certain constraints, such as the probability of operations issues with equipment malfunction and/or weather issues may be more difficult to predict; therefore, these issues are not included or embodied in the math.

In practice, the design model 930 may input or access configuration options, such as one or more options for different configurations for drilling and construction. Example options include values for different numbers of wells, values for different well spacing, values for different well configurations (e.g., different horizontal depths; different pipeline widths; different fracturing configurations), values for different compressors (e.g., compressors with different pumping capabilities and associated costs), and/or values for different surface piping (e.g., different piping widths). The design model 930, using the reservoir interconnectivity model 932 (which may indicate the response from the subsurface) and the drilling+construction optimization model 934 (which may be constrained in one or more ways as described above), may select a drilling+construction configuration, which may include values for one or more parameters associated with the design stage, including any one, any combination, or all of: the number of wells to drill; the well spacing for the wells drilling; the well configuration; the value for the compressor; and the value for the surface piping.

FIG. 9C is a block diagram 940 of the operations model 950 for optimization during one or more operation stages, such as the primary depletion stage and/or the gas injection stage. The operations model 950 may be configured for optimization during the operations stage (examples of which are shown as annual planning model 1022, cycle operations model_1 1024, cycle operations model_2 1026, and daily operations model 1030, 1032, 1034 in FIGS. 10-12 ). In one or some embodiments, the reservoir interconnectivity model 932 in operations model 950 may be the same or an updated version of the reservoir interconnectivity model 932 used in the design model 930, as discussed below. Further, the optimization model 914 may be tailored to a specific stage of hydrocarbon management, such as the drilling+construction stage, and shown as operations optimization model 952. Similar to the design model 930, the operations model 950 may include one or more constraints in selecting the optimal values for the one or more operations stages with the constraints including any one, any combination, or all of: practical constraints; budgetary constraints; or best practices/intuition.

In practice, the operations model 950 may input configuration options, such as one or more options for different configurations for gas injection, including gas injection into the tubing of wells (e.g., for huffing) and/or gas injection into the annulus (e.g., for artificial lift). Example options include, without limitation, any one, any combination, or all of: the number of cycles of huffing-and-puffing; the length of time of the cycles; which wells to select as injector well(s) for the gas; the injection rate; the injection volume; the duration of injection; the sequence of which injector wells to inject in; the type of gas for injection; for injector well(s) and/or offset wells, whether to artificially lift, and if so, the rate and duration of artificial lift; which offset wells to cap or plug (and when to cap/how long to cap) and which not to cap; or timing for artificial lift in injector well(s) and/or offset well(s).

The operations model 950, using the reservoir interconnectivity model 932 (which may indicate the response from the subsurface) and the operations optimization model 952 (which may be constrained in one or more ways as described above), may select the gas injection configuration, which may include values for one or more parameters associated with the gas injection stage, including the number of wells to drill, the well spacing for the wells drilling, the well configuration, the value for the compressor, and the value for the surface piping.

FIG. 9D is a block diagram 960 of the huff and puff system 970. As discussed above, various stages of the system may be modeled. As one example, the huff and puff stage within the gas injection stage may comprise injecting gas into the tubing of an injector well. The huff and puff system 970, from a physical standpoint, may be modeled via one or more equations, such as illustrated as follows:

S(y(x,z),x,z)=0  (14)

v=D(y)+ϵ(x,z)  (15)

-   -   where S represents the “true” physical, chemical, and/or         thermo-dynamical process, which may be generally unknown         exactly. S may include any one, any combination, or all of:         geological geometry; rock properties; fluid properties; one,         some or each well location; configuration and geometry; wells         relative locations; compression capacity; or well type (e.g.,         injection producing);     -   x denotes system input, which may include any one, any         combination, or all of: injection rates; injection duration; or         injection gas properties;     -   z are discrete/categorical/binary design variables such as any         one, any combination, or all of: well/pipelines/surface network         topology; designation of wells to be either injector or         producer; number of wells; number location; or size of         compressors;     -   y denotes the system state (e.g., quantity of interest), which         may include reservoir pressure;     -   D represents observation/measurement model. In case of no direct         measurement of system state y,     -   D may represent a relationship between y and quantities that may         be measured;     -   v denotes quantities that may be measured (e.g., downhole         pressure or three-phase rates at wellhead or separator); and     -   ϵ denotes observation errors.

As mentioned, S may generally not be precisely known. Thus, one may assume that there is a computational model (e.g., mathematical, statistical, machine-learning) that may represent the system S according to the following:

S(y(x,z),x,z)={tilde over (S)}(y(x,z),x,z,θ)+δ(x,z,θ)  (16)

-   -   where S denotes the computational model (e.g., mathematical,         statistical, machine-learning) representing S parameterized by         θ.

θ denotes modeling aspects needed to run the computational models, which may include any one, any combination, or all of: geological geometry; rock properties; fluid properties; one, some or each well location; configuration and geometry; wells relative locations; compression capacity; or well type (e.g., injection producing).

δ denotes model bias or discrepancy (e.g., functional discrepancy or bias correction) due to unknown or mis-modeled physical or chemical aspects of the process. In this regard, δ may account for any one, any combination, or all of physical, thermal, or chemical reactions. As one example, when CO₂ is injected, there is a potential for a reaction, such as a thermal reaction. As another example, δ may account for calcification, whereby CO₂ may react with water or calcium to form calcium carbonate. Thus, this term may indicate that {tilde over (S)} has systematic imperfections, even under its best tuned parameter θ*. One may assume that reasonable correction to {tilde over (S)} may be learned through δ. Further, δ may be determined or learned algorithmically from the data.

The same argument may apply for observation model D. D may depend on either reservoir properties (e.g., any one, any combination, or all of geological geometry, rock properties; and fluid properties) in case of bottom-hole pressure being the observable quantities or well properties (e.g., any one, any combination, or all of diameter, friction factor, or fluid properties) in case of fluid rate production being the observable quantity.

Thus, in summary:

$\begin{matrix} {{{\overset{˜}{S}\left( {{y\left( {x,z} \right)},x,z,\theta} \right)} + {\delta\left( {x,z,\theta} \right)}} = 0} & (17) \end{matrix}$ $\begin{matrix} {v = {{D\left( {y,\theta} \right)} + {\epsilon(x)}}} & (18) \end{matrix}$ ${{where}\theta} = \left\{ {\begin{matrix} \theta_{G} \\ \theta_{F} \end{matrix};} \right.$

-   -   with θ_(G) being geologic and rock property parameters; and     -   with θ_(F) being fluid properties parameters;

${{where}x} = \left\{ {\begin{matrix} x^{D} \\ x^{OP} \end{matrix};} \right.$

-   -   with x^(D) being the well and huff and puff system design; and     -   with x^(OP) being the well and huff and puff operations         variables.

Thus, equations (17) and (18) provide one example representation in equation form of fluid movement. Other representations are contemplated, such as based on a reservoir model or a reservoir simulation. Henceforth, for simplicity, the dependence of y on x and z is suppressed in the above equations for purposes of compaction.

-   -   y is reservoir pressure P;     -   x represents any one, any combination, or all of gas injection         rate, injection duration, well type (e.g., injector well,         producing well);     -   v is either bottom hole pressures or fluid rates q; and     -   P₀ is initial reservoir pressure (e.g., the reservoir pressure         at time 0).

Further, the system may be dynamic and therefore dependent on time as shown in the following:

$\begin{matrix} {{\overset{˜}{S}\left( {y,x,z,\theta} \right)} = {{V\frac{dP}{dt}} - {f\left( {{P(t)},{q(t)},z} \right)}}} & (19) \end{matrix}$ $\begin{matrix} {{D\left( {y,\theta} \right)} = {F_{cd}\frac{\Delta P}{\mu}}} & (20) \end{matrix}$ ${{{where}F_{cd}} = {ae^{b\overset{¯}{P}}}};$

-   -   t represents time; and     -   f(P, q, z) may comprise any one, any combination, or all of a         physics-based model, a data-driven model, or a hybrid model.

In one example, the system modeling may be represented as follows (with a more general set of equations than those listed above):

$\begin{matrix} {{V_{1}\frac{dP}{dt}} = {{P_{1}\left( {q_{inj} - {\sum q}} \right)} + \delta_{1}}} & (20) \end{matrix}$ $\begin{matrix} {{V_{2}\frac{dP}{dt}} = {{P_{2}\left( {q_{inj} - {\sum q}} \right)} + \delta_{2}}} & (21) \end{matrix}$ $\begin{matrix} {{V_{3}\frac{dP}{dt}} = {{P_{3}\left( {q_{inj} - {\sum q}} \right)} + \delta_{3}}} & (22) \end{matrix}$ $\begin{matrix} {{q(t)} = {F_{cd}\frac{\Delta{P(t)}}{\mu}}} & (23) \end{matrix}$ $\begin{matrix} {F_{cd} = {ae^{b\overset{¯}{P}}}} & (24) \end{matrix}$ $\begin{matrix} {{P(0)} = {P_{0}.}} & (25) \end{matrix}$

As such, the above equations may indicate how pressure (P₁, P₂, P₃) at the bottomholes of different wells is changing with respect to time for a given injection rate(s) (q_(inj)). As discussed below (see FIG. 17 ), the determined pressures (as a function of the given injection rate(s)) at the bottomholes of the various wells may in turn be used to determine pressures at different locations within the subsurface separate from the bottomholes, such as at the reservoir. Merely by way of example, various mathematical operations (e.g., averaging) may be used in order to determine the pressure at the reservoir. Alternatively, or in addition, properties of the subsurface, such as porosity and/or permeability, may be used to determine the pressure at the reservoir.

In practicality, oil may be in tiny holes within rock in the reservoir. Increasing pressure in the reservoir may result in: (1) opening gateways within the rock to release the oil in the rock in the reservoir; and (2) creating a pressure gradient so that the oil can move to the bottomholes of one of the wells (e.g., the pressure is higher within the reservoir than at the bottomholes of one of the wells). Further, injecting gas into the reservoir may comprise huff and puff, resulting in two periods: (1) injecting fluid; and (2) after injecting fluid, stopping injecting fluid. While injecting fluid, the pressure may be highest at the bottomhole at the injector well(s). After injecting has stopped, and the injector well(s) may pump oil, the reservoir, which has had its pressure increase, may release some of its pressure so that oil in the reservoir moves toward lower pressure regions, such as to the bottomholes of the injector well(s) and/or the offset wells. In this way, some of the gas that was previously injected into the reservoir will be reproduced back (e.g., the oil that is pumped out may include some of the gas that was injected previously into the reservoir), thereby enabling recovery of at least some of the gas that was previously injected.

With regard to q_(inj), the gas injected into the reservoir via the injector well may change the pressure at the bottomhole injector well (as discussed above), and in turn, the pressure differential between the bottomholes of the injector well versus the offset well. More generally, the pressure at various points in the reservoir may likewise change. As discussed above, one option is to include a model having a set of partial differential equations that are very detailed, enabling modeling at every point in the subsurface and enabling modeling of the geology (e.g., permeability and/or porosity). However, to model such details of the pathways in the subsurface may be very computationally expensive. Alternatively, a more focused and limited model, such as the interwell connectivity model, may be based on a more limited set of inputs, and may be focused on a limited set of criteria (e.g., pressure, such as average pressure, at various parts of the subsurface, such as in the reservoir), thereby correlating any one, any combination, or all of the more limited set of inputs with any one, any combination, or all of a limited set of outputs (e.g., pressure and/or production). In one or some embodiments, the correlation may be based on the interwell connectivity metric. In this way, the more focused interwell connectivity model may provide the basis for an approximate pressure changes within the reservoir responsive to the huff and puff, enabling estimation of the reservoir performance. Further, as shown in the equations above, the interwell connectivity may be obtained in a simpler manner, such as by using F_(cd), which is dependent (e.g., exponentially dependent) on average pressure (P), as shown in Equation (24).

In turn, the equations above may determine the production, such as the production from the offset well during huff, by determining production (q), which in one embodiment, may be time dependent (q(t)). Further, the equations above may provide a direct correlation between the gas injected (q_(inj)) and the production (q), in effect providing a more direct connection between the controllable input(s), such as gas injected, with the one or more desired outputs, such as production.

As discussed above, an improvement or optimization model may be paired with a reservoir model. Further, as discussed above, various types of models are contemplated to represent the reservoir, including any one, any combination, or all of: a more-inclusive reservoir simulation model; a simplified model (as shown in the equations above, such as correlating q_(inj) and q, such as based on an interwell connectivity metric); or a modified model (e.g., a machine learning model, such as a neural network that represents the subsurface). In one or some embodiments, the simplified model may include a correction factor (e.g., δ) to enable a less computationally intensive solution than a reservoir simulation model in determining the response in the reservoir to fluid injection.

Further, in one or some embodiments, the optimization model may have integrated therein any one, any combination, or all of: best practices; intuition; or knowledge, which may be manifested in rules or algorithmically. In particular, the optimization model may include one or more constraints (e.g., practical constraints and/or budgetary constraints) so that the generated outputs conform to expectations.

FIG. 10 is a graph 1000 of hydrocarbon extraction from an injector well versus time in the primary depletion stage and the huff and puff stage (including multiple cycles of huff and puff in the injector well and multiple artificial lift stages), and block diagrams of the model calibration 1010, 1012, 1014, 1016 of the reservoir model in the various stages. FIG. 11 is a graph 1100 of hydrocarbon extraction from an offset well (that is not plugged during huffing) versus time in the primary depletion stage and the huff and puff stage (including multiple cycles of huff and puff in the injector well and multiple artificial lift stages), and block diagrams of the model calibration of the reservoir model in the various stages. FIG. 12 is a graph 1200 of hydrocarbon extraction from both injector well(s) and offset well(s) versus time in the primary depletion stage and the huff and puff stage (including multiple cycles of huff and puff in the injector well(s)), and block diagrams of the model calibration of the reservoir model in the various stages. In this regard, FIG. 12 is a graph summing the hydrocarbon extraction from each injector well(s) and offset well(s).

FIGS. 13A-C are illustrations 1300, 1350, 1360 showing different stages of operation of a well, including during production without any gas injection (e.g., no gas injection through the tubing 1312 and no gas injection in the annulus, which is the region between the production casing 1310 and the tubing 1312) shown in FIG. 13A, during production with artificial lift (e.g., gas injected into the annulus) shown in FIG. 13B, and during gas injection through the tubing (e.g., huff) shown in FIG. 13C.

In practice, a wellbore may be drilled in order to aid in the exploration and recovery of various natural resources, such as oil and/or gas. The wellbore may be the hole that forms the well. A wellbore may be encased by materials such as steel and cement, or it may be uncased. As shown, the system includes the tubing 1312, which may be gas tight, and a production casing 1310, which may include a vertical section and a horizontal section. The tubing 1312 and the production casing 1310 may be formed as two concentric circles, with the volume in between forming the annulus. Further, hydraulic fractures 1320 may be formed from the production casing 1310. During production with natural flow (e.g., without any gas injection including huffing or artificial lift), hydrocarbons flow into the hydraulic fractures 1320 (shown as arrows 1330), then through the horizontal section of the production casing 1310 (shown as arrows 1332), and then through the tubing 1312 (shown as arrows 1334), and ultimately out of the tubing 1312 (shown as arrow 1336).

As discussed above, injecting fluid, such as gas, through the tubing 1312, into the wellbore (illustrated as gas injection through tubing 1362 which then travels via arrows 1364, 1366 from the wellbore into the hydraulic fractures, and from the hydraulic fractures into the rock matrix (shown as arrows 1368), thereby travelling to the subsurface in the reservoir. In this way, the injected gas may increase the pressure in the regions close or proximate to the hydraulic fractures 1320. Thus, in one or some embodiments, the injection of gas through tubing 1312 (an example of huffing) may result in the gas being injected into the rock matrix. In particular, the rock matrix comprise tightly packed rocks into which gas is injected, which in turn may assist in hydrocarbon flow trapped in the tightly packed rocks.

Alternatively, or in addition, the gas may be injected into the annulus. As shown in FIGS. 13A-C, the gas injected in the annulus 1352 (shown traversing by arrows 1354) cannot go beyond the packer 1316, which may comprise an O-ring that may separate the casing from the rest of the subsurface reservoir. The gas flows through gas lift valves 1314 into tubing 1312, which may, in turn, lift the fluid 1334 upward. In effect, the gas injected in the annulus 1352 and then into tubing 1312 makes the fluid in the tubing 1312 lighter and may be used when production plateaus or decreases. Thus, gas injected into the tubing 1362 is in contrast to artificial lift, in which the gas is injected in a different manner (e.g., through the annulus as opposed into the tubing 1312), in which the gas remains localized (only in the annulus or the tubing since the gas cannot travel past the packer 1316 as opposed to ultimately into the reservoir), and in which the gas is mixed directly with the hydrocarbons in the tubing 1312 to make them lighter (as opposed to injecting the gas into the reservoir in order to cause movement of hydrocarbons within the reservoir).

As discussed above, additional data may be obtained at one or more times or time periods, such as during the primary depletion and/or subsequent cycles. In turn, the additional data may be used to update one or more models. For example, the analytical model 200 may be updated based on the additional data obtained. In particular, one or more parts of the analytical model 200, such as any one, any combination, or all of parameter(s), bias, or time lag(s) may be updated. In this regard, the analytical model 200 may comprise an initial model (e.g., modeling parameters, bias, time lag(s) via equations(s)) and may be tuned using additionally obtained data (e.g., via primary depletion and/or via cycle(s)).

Merely for example, FIGS. 10-12 illustrates that at various stages, δ and θ may be updated. Specifically, prior to obtaining data from the primary depletion stage, the model may include one or more parameters, such as δ_(prior) and θ_(prior) As discussed above, δ denotes model bias or discrepancy and θ denotes modeling aspects, such as any one, any combination, or all of: geological geometry; rock properties; fluid properties; one, some or each well location; configuration and/or geometry; wells relative locations; compression capacity; or well type (e.g., injection producing). In this regard, δ may encompass various parts that are not found in the present model, but which may be updated through the various model calibrations, such as illustrated in the different cycles. Further, δ may be dependent on one or more variables, such as any one, any combination, or all of time, fluid rates (e.g., injection rate q), or pressure. As shown in FIG. 10 , additional data obtained during the primary depletion stage (denoted as Data_0, which may comprise production data, such as illustrated in curves 1040, 1120, 1220) may be input to model calibration 1010 in order to update the model, and thus produce updated δ and θ, shown as δ₀ and θ₀. For example, the actual production (as reflected in curves 1040, 1120, 1220) may be compared with the estimated curves from the model, with the discrepancy used by model calibration 1010 in order to update the model. This updating process may be performed periodically, such as responsive to obtaining data in cycle 1 (with the additional data obtained during the cycle 1 stage (denoted as Data_1, which may comprise production data, such as illustrated in curves 1041, 1043, 1045 during natural flow and in curves 1042, 1122, 1222 during artificial lift) and δ₀ and θ₀ may be input to model calibration 1012 in order to update the model, and thus produce updated δ and θ, shown as δ₁ and θ₁), in cycle 2 (with the additional data obtained during the cycle 2 stage (denoted as Data_2, which may comprise production data, such as illustrated in curves 1044, 1124, 1224) and δ₁ and θ₁ may be input to model calibration 1014 in order to update the model, and thus produce updated δ and θ, shown as δ₂ and θ₂), and/or in cycle 3 (with the additional data obtained during the cycle 3 stage (denoted as Data_3, which may comprise production data, such as illustrated in curves 1046, 1126, 1226) and δ₂ and θ₂ may be input to model calibration 1012 in order to update the model, and thus produce updated δ and θ, shown as δ₃ and θ₃).

For example, in one or some embodiments, model calibration 1010, 1012, 1014 may comprise a model update module configured to update the one or more parts of the model based on additional data obtained (e.g., from drilling to primary depletion, to cycle 1, cycle 2, etc.). In a particular embodiment, the model update module may update any one, any combination, or all of: (i) model parameters (e.g., V, a, b); (ii) model bias (e.g., to incorporate missing or incomplete physics, such as A); or (iii) time lag(s) (e.g., time delay τ, time shift, etc.).

For example, in determining the values of the model parameters (e.g., any one, any combination, or all of: the length of time; timing; or rate of huff of the huff period and/or any one, any combination, or all of: the length of time; timing; or rate of the artificial lift period), the models may consider may consider one or more time lags, including any one, any combination, or all of: a time delay indicative of: (1) time delay indicative of a shift in the effect of an input on the system's output dynamic response; or (2) time shift used to determine improved or optimal timing for gas lift.

${{V_{1}(t)}\frac{d{P_{1}(t)}}{dt}} = {{P_{1}\left( {{q_{inj}\left( {t - \tau} \right)} - {\sum{q(t)}}} \right)} + {\delta_{1}(t)}}$

Merely for purposes of illustration, consider t=5 and τ=3. If injection is performed at t=2, the effects, due to the time lag, may be seen at time t=5. Knowing the time lag assists in configuring the injection strategy. τ may generally be unknown, but may be predicted. In this regard, τ may initially be estimated and iteratively updated.

With regard to (1), the time delay τ may be expressed as a time shift in the input (e.g., control) variable(s), such as gas injection rate (q_(inj)). Merely by way of example, one manifestation of the time lag for (1) is illustrated in FIG. 6 as Δt (see resulting in Δt₁ and resulting in Δt₂) which may measure the lag in an offset well responsive to a pressure change in the injection well. In this regard, the modeling may identify the time discrepancy between system stimulus (e.g., the huff phase) and system response (e.g., the puff phase), in turn allowing for more accurate modeling of production phase, such as in cycles 1, 2, and 3.

In this regard, the response lag may be indicative of a time delay from injecting gas into the rock and the effect of the injection manifested in the pressure response in the offset wells (see, e.g., FIG. 6 ). In other words, the lag may be due to the reservoir's delayed response to gas injection.

For (1), there may be any one, any combination, or all of the following three components: (a) delay of pressure response to injection; (b) delay to unsoldered temporal components; or (c) time it takes fluids to transport between wells.

As discussed above, various equations such as Equations (4)-(10), may relate to the response lag. In particular, modeling (c) may include Equations (8)-(9). Further, modeling both (a) and (b) may be included in the time delay/lag (see τ in the Equations above). In this regard, the delay for (1) may be a function of any one, any combination, or all of: rock properties; location of the offset wells relative to injector well; chemistry of the injected gas (e.g., rich vs. lean gas); or fluid properties.

With regard to (2), the time shift needed to determine an improved/optimal timing for gas lift may be reflected in an expanded system models beyond Equations (4)-(10). In this way, the time shift may be used in order to determine the delay of the gas lift in the well (e.g., until the gas lift is needed). This is illustrated, for example, in FIG. 11 . In particular, FIG. 11 is for control of an offset well. Huff 1 indicates that an injector well is injected with gas. The offset well (shown in FIG. 11 ) begins cycle 1 with an artificial lift for a length of time based on the delayed effect of the huff (e.g., the delay in the gas injected in the injected well affecting the offset well).

Further, the model, such as the analytical model 200, may be used in combination with (such as embedded within or in conjunction with) an improvement or optimization model that may be tailored for one or more stages. For example, FIG. 10 illustrates design model 1020, which may include both the analytical model 200 and the improvement or optimization model tailored to the design phase, and is configured to optimize one or more aspects associated with the drilling+construction phase. As discussed above, the design model 1020 may select parameters for drilling+construction, such as; the number of wells to drill; the well spacing for the wells drilling; the well configuration; the value for the compressor; and the value for the surface piping.

In one embodiment, an operator inputs the constraint(s) of the system, such as the maximum oil rate constraint 1210. Alternatively, the design model 1020 determines the constraint(s) of the system, such as the maximum oil rate constraint 1210. Regardless, the design model may use the constraints of the system, the interwell connectivity metric, and the potential values for artificial lift and huff and puff in order to design the system itself (e.g., the parameters for drilling and/or construction of the wells, the mechanical hardware (e.g., compressor(s)); the piping; etc.). In this way, the design of the system comports with the constraint(s). Specifically, the design may avoid being oversized (e.g., the system being design for greater capacity than the maximum oil rate constraint 1210) so that the production never approaches the maximum oil rate constraint 1210.

In this regard, the design model 1020 is operated based on a limited understanding of the subsurface to determine the parameters of the system. In practice, the design model 1020 may generate a current best estimate as to the amount of hydrocarbons for extraction from the reservoir, determine a budget for drilling/construction of the system (e.g., $200 million for a specific pad), and select, from ranges of potential values, the values of the system (e.g., selecting the number of wells from a range of 5-20 for the maximum number of wells; select the piping from a range of piping from 3″ diameter to 5″ diameter). In one or some embodiments, the selected values may then determine the maximum oil rate constraint 1210.

Typically, production (e.g., barrels per day) decreases monotonically over time, as illustrated in curves 1040, 1120, 1220 without a gas injection stage. In contrast, the model(s) may configure the gas injection stage, such as huffing and/or artificial lift, in order to increase the production. In one or some embodiments, the gas injection stage includes multiple cycles, with the peak production in the different cycles being different (e.g., peak production increasing from cycle 1, to cycle 2, to cycle 3, with the peak production in cycle 3 being closest to the maximum oil rate constraint 1210, as shown in FIG. 12 ). Thus, in one or some embodiments, the peak production approaches or meets the maximum oil rate constraint 1210 in at least two stages, such as in the primary depletion stage and in at least one of the cycles in the gas injection stage (e.g., in cycle 3). This is in contrast to a typical extraction without gas injection in which the maximum oil rate constraint 1210 is only reached once (during primary depletion). In this way, the design of the system, using the design model 1020, may be optimized. After drilling and construction in which the system is built, the model(s) may then optimize operation.

At a certain time (which may be determined by a primary depletion model, not shown in FIGS. 10-12 ), the primary depletion stage may be stopped in order to transition to the gas injection stage, in which gas is injected into tubing (e.g., huff and puff) and/or gas is injected into the annulus (e.g., artificial lift). As shown in FIGS. 10-12 , the gas injection stage includes a plurality of cycles, each of which may include one or both of huff and puff and artificial lift (as shown in FIGS. 10-12 , huff and puff and artificial lift are used in each cycle, although any combination of huff and puff and artificial lift in the different cycles are contemplated).

Thus, in one or some embodiments, the gas injection stage includes one or both of: (i) huff and puff (e.g., gas injected into the reservoir, such as via tubing 1312); or (ii) artificial lift (e.g., gas not directly injected into the tubing but travels into the tubing, such as via check valve(s) 1314). In one or some embodiments, for the same injector well, the same values for all of the parameters are used for huffing in the different cycles. Alternatively, for the same injector well, different values may be used for one, some, or all of the parameters of huffing in the different cycles (e.g., in order to increase production, such as illustrated in cycle 1, cycle 2, and cycle 3, different parameters, such as any one, any combination, or all of increased volume of gas injected, increased rate, or increased length of time may be used).

In one or some embodiments, for different injector wells: the same values for all of the parameters are used for huffing in the same cycle and/or in different cycles. Alternatively, for the different injector wells, different values may be used for one, some, or all of the parameters of huffing in the same cycle and/or in different cycles (e.g., because different interwell connectivity metrics may be present, the values for huff and puff for a first injector well may be different than for a second injector well, such as any one, any combination, or all of different timing of injection, different rates of injection, different lengths of time of injection, or different total volumes of injection).

In one or some embodiments, for the same well, the same values for all of the parameters for artificial lift are used for performing the artificial lift in the different cycles. Alternatively, for the same well, different values for one, some, or all of the parameters may be used to perform the artificial lift in the different cycles (e.g., in order to increase production, such as illustrated in cycle 1, cycle 2, and cycle 3).

In one or some embodiments, for different wells, the same values for all of the parameters for artificial lift are used for performing artificial lift in a same cycle and/or in different cycles. Alternatively, different values for one, some, or all of the parameters for artificial lift are used for performing artificial lift in a same cycle and/or in different cycles (e.g., because different interwell connectivity metrics may be present, the values for artificial lift for a first well may be different than for a second well, such as any one, any combination, or all of: (i) different numbers of artificial lifts in a single cycle (e.g., injector well or plugged offset well subject to a single artificial lift whereas an unplugged offset well is subject to multiple artificial lifts); (ii) different timing of artificial lift; (iii) different rates of artificial lift; (iv) different lengths of artificial lift; or (v) different total volumes of artificial lift).

In one or some embodiments, for a respective well subject to multiple artificial lifts in a single cycle, the same values for all of the parameters may be used for each artificial lift within the same cycle. Alternatively, different values for one, some, or all of the parameters may be used for each artificial lift within the same cycle (e.g., because of the effect of gas injected via injector well(s) and different interwell connectivity metrics, the parameters for the different artificial lifts may vary).

Further, as discussed above, within a respective cycle and/or across different cycles, a respective well may have any combination of the following: zero, one, or more than one huff stages; zero, one, or more than one natural flow stages; and zero, one, or more than one artificial lift stages. In the event that the respective well is not an injector well, zero huff stages are performed. In this instance, for example, one or more artificial lift stages may be performed along with one or more natural flow stages (e.g., see FIG. 11 in which artificial lift periods 1110 and 1140 sandwich natural flow period 1130). As discussed above, the values for the parameters for the artificial lift stages and/or the natural flow stages may be the same or different. In the event that the respective well is an injector well, one or more huff stages may be performed, with zero, one, or more than one artificial lift stages and zero, one, or more than one natural flow stages used as well (e.g., a sequence of a huff stage, a natural flow stage, and an artificial lift stage). The values for the parameters for the huff stage and/or the artificial lift stages may be the same or different, as discussed above.

Further, within a respective cycle and/or across different cycles, different wells may have the same or different combinations of huff stages, natural flow stages, and artificial lift stages. Merely by way of example, in the event that a first well is selected as an injector well and a second well is not selected as an injector well, the first well is assigned at least one huff stage (and optionally one or more natural flow stages and one or more artificial lift stages) whereas the second well is not assigned a huff stage. Further, the second well may be assigned one or more artificial lift stages with a respective cycle (such as at least two artificial lift stages, see FIG. 11 ), whereas the first well may be assigned only a single artificial stage within the respective cycle. Conversely, in the event that the first well and the second well are both selected as injector wells, both the first well and the second well may be assigned at least one huff stage (and optionally one or more natural flow stages and one or more artificial lift stages). In one or some embodiments, the values assigned to the parameters for the huff stage, for the natural flow stage (e.g., the length of time for natural flow) and for the one or more artificial lift stages for the first well and the second well may be the same or may be different. In this way, the operations for a respective well or a respective group of wells may be improved or optimized using the model(s).

Thus, in order to determine the parameters of the gas injection stage, a gas injection model, which may include both the analytical model 200 and the improvement or optimization model tailored to the gas injection stage, may be used. In one embodiment, a single model is used to select the parameters for the entire gas injection stage. Alternatively, as shown in FIG. 10 , a plurality of models are used to select the parameters for the gas injection stage. For example, the gas injection stage may include one or more models, such any one, any combination, or all of: an overall operation model (e.g., annual planning model 1022) configured to determine parameters for multiple cycles, such as all cycles; one or more cycle operation models (e.g., cycle operations model_1 1024; cycle operations model_1 1026) configured to select the parameters for a respective cycle; or a sub-cycle operations model (e.g., daily operations model 1030, 1032, 1034 or other sub-cycle, such as weekly, monthly, etc.).

For example, the annual planning model 1022 may be configured to optimize one or more aspects associated with huffing and puffing and/or artificial lift during a predetermined time period, such as annually. Further, the annual planning model 1022 may be configured to determine the parameters for multiple cycles, such as each of cycle 1, cycle 2, and cycle 3. As discussed above, additional data may be used to update the model. In this regard, after cycle 1, the model may be updated (see model calibration 1012), which may then be used for cycle operations model_1 1024, which may be used to determine the parameters for cycle 2 (with the parameters determined by cycle operations model_1 1024 being different in one or more aspects than the parameters determined by annual planning model 1022 for cycle 2 due to the updating of the model).

Further, within a respective cycle, daily operations model 1030, 1032, 1034 may be configured to improve or optimize operations on a predetermined basis, such as daily. By way of example, the system may have certain constraints, such as a limit on the amount of gas to inject and/or a limit on the amount of oil that should be produced (e.g., see maximum oil rate constraint 1210, discussed below). The daily operations model 1030, 1032, 1034 may be configured to control the system such that the constraints are met efficiently (e.g., limit the amount of artificial lift and/or huffing; choke back production).

FIG. 10 illustrates a plurality of cycles (such as cycle 1, cycle 2, and cycle 3) in which injector well(s) may include a huff period and a gas injection period, with one or both of a natural flow period (in which no gas is injected) and artificial lift (in which gas is injected into the annulus). In particular, a huff period 1060, 1070, 1080, in which gas is injected as shown by 1050, 1052, 1054 during the respective huff period 1060, 1070, 1080, followed by at least one natural flow period 1064, 1074, 1084, and at least one artificial lift period 1066, 1076, 1086. As shown in FIG. 10 , the sequence comprises the huff period, the natural flow period, and then the artificial lift period. For example, because of the gas injected during the huff period into the reservoir, the fluid (e.g., the oil) in the reservoir may be lighter so that artificial lift is unnecessary to extract the hydrocarbon from the reservoir immediately after the huff period. However, after a certain time (due to the dispersal of the gas in the reservoir as modeled by the interwell connectivity metric), an artificial lift period may be performed after the natural lift period. Alternatively, within a respective cycle, for an injector well, the huff period may only be followed by the natural flow period. Still alternatively, for the injector well, the huff period may only be followed by the artificial flow period. Yet alternatively, for the injector well, one or more huff periods within a cycle may be followed by one or more natural flow periods and one or more artificial lift periods. Because the gas is injected during the huff period 1060, 1070, 1080, the respective injector well does not produce. However, after which, the respective injector well produces, as shown by curves 1042, 1044, 1046.

In one or some embodiments, the models, such as annual planning model 1022, cycle operations model_1 1024, and/or cycle operations model_2 1026 may determine the sequence of periods and/or the length of time for the periods, such as the sequence and/or length of time for any one, any combination, or all of: the huff period; the natural flow period; or the artificial lift period. For example, the models may recommend a huff period (huff 1 1060, huff 2 1070, huff 3 1080) followed by a puff period (puff 1 1062, puff 2 1072, puff 3 1082). Further, the models may recommend one or more natural flow periods 1064, 1074, 1084 and one or more artificial lift periods 1066, 1076, 1086 within a respective puff period (puff 1 1062, puff 2 1072, puff 3 1082). As shown in FIG. 10 , within a respective puff period (e.g., puff 1 1062), a natural flow period (e.g., natural flow 1064) is followed by an artificial lift period (e.g., artificial lift 1066). In this regard, in one or some embodiments, the huff period may be followed by the natural flow period, and then followed by the artificial lift period, as shown in FIG. 10 . Generally speaking, immediately after the huff period (in which gas has been injected into the reservoir via tubing), the reservoir may not need any artificial lift. Thus, the natural flow period may immediately follow the huff period. Further, over time, the gas injected during the huff period, providing a temporary lift thus resulting in the subsequent natural flow period, may disperse, which in turn may necessitate a subsequent artificial lift period.

Further, the models may determine the length of each respective period, such as the length of any one, any combination, or all of: the huff period; the natural flow period; or the artificial lift period. Merely by way of example, the models may determine the length of time of huff 1 1060 to improve or optimize the hydrocarbon extraction during puff 1 1062. Alternatively, or in addition, the models may determine the length of time of natural flow 1064 and/or artificial lift 1066 during puff 1 1062 to improve or optimize the hydrocarbon extraction.

As such, in one or some embodiments, the models may determine both the sequence of the periods and the length of the respective periods, considering any one, any combination, or all of: the amount of gas for injection during the huff period (e.g., considering the interwell connectivity metric affecting the flow of gas in the subsurface); the length of time for the natural flow period (considering, based on the interwell connectivity metric, the dispersal rates of the injected gas); or the length of the artificial flow period.

As discussed above, FIG. 11 is a graph 1100 of hydrocarbon extraction from an offset well that is not plugged during huffing. Similar to FIG. 10 , design model 1020 may generate the parameters for the drilling+construction for one, some or all of the wells, including one or both of the injector well(s) and the offset well(s). After which, primary depletion occurs in the offset well, as shown in curve 1120, illustrating the amount of hydrocarbon extracted over time from the respective offset well. At a certain time (which may be determined by a primary depletion model), the primary depletion stage may be stopped in order to transition to the gas injection stage (e.g., injecting gas into tubing of one or more injector wells and/or injecting gas into the annulus). As shown, the gas injection stage includes cycle 1, cycle 2, and cycle 3 with the hydrocarbon extracted in the respective cycles shown as curves 1111 (production during artificial lift period 1110), 1113 (production during artificial lift period 1112), 1115 (production during artificial lift period 1114), 1131 (production during natural flow period 1130), 1133 (production during natural flow period 1132), 1135 (production during natural flow period 1134), 1122 (production during artificial lift period 1140), 1124 (production during artificial lift period 1142), 1126 (production during artificial lift period 1144).

Thus, as shown in FIG. 11 , after the primary depletion stage, the system may enter the gas injection stage Similar to the injector well(s), the models, such as annual planning model 1022, cycle operations model_1 1024, or cycle operations model_2 1026, may determine the sequence and/or the length of time for the periods within a respective stage or cycle. By way of example, FIG. 11 illustrates within a respective cycle, the following sequence: artificial lift period 1110, 1112, 1114; natural flow period 1130, 1132, 1134; artificial lift period 1140, 1142, 1144. Thus, unlike injector wells, the beginning of a respective cycle for offset wells that are not plugged is the artificial lift period. Further, FIG. 11 illustrates that within a cycle a respective stage may occur at least once (e.g., the natural flow period 1130, 1132, 1134) or may occur at least more than once (e.g., a first artificial lift period 1110, 1112, 1114 and a second artificial lift period 1140, 1142, 1144). Moreover, in the instance where a respective stage occurs more than once within a cycle, the length of time for the respective stage may be the same or may be different (e.g., the first artificial lift period 1110, 1112, 1114 is shorter in time than the second artificial lift period 1140, 1142, 1144).

In one or some embodiments, because the primary depletion stage does not inject gas (either into the reservoir via tubing or into the annulus), the model(s) may determine a potential need for artificial lift (e.g., injecting gas into the annulus) for offset wells that are not plugged after the primary depletion stage (such as immediately after the primary depletion stage). See 1110, 1112, 1114. Further, the model(s) may determine a length of time of the artificial lift stage(s). For example, as shown in FIG. 11 , the artificial lift period 1110, 1112, 1114 for a respective offset well is at least partly coextensive with the huff period 1060, 1070, 1080 for a respective injector well. In one or some embodiments, the length of time for the artificial lift period for a respective offset well is shorter than the huff period for a respective injector well (see, for example, FIG. 11 in which dashed line 1190 shows that huff 1 1060 (for the injector well) is for a longer time than artificial lift 1110 for offset well). Alternatively, the length of time for the artificial lift period for a respective offset well is longer than the huff period for a respective injector well. Alternatively, or in addition, the model(s) may determine an intensity of the artificial lift. Specifically, in one embodiment, the model(s) may determine within a respective artificial lift period, the rate of gas injected into the annulus remains constant. In an alternate embodiment, the model(s) may determine within the respective artificial lift period to vary the rate of gas injected, such as initially inject at a higher rate (e.g., at the beginning of the huff period 1060, 1070, 1080) until a predetermined time and then inject gas at a reduced rate until the artificial lift period ends.

In particular, the model(s) may determine the length of time for a respective artificial lift period for an offset well based on the interwell connectivity metric of the respective offset well with respective injector well(s). As one example, a higher interwell connectivity metric, indicative that there is a greater fluid connection between the respective offset well and the respective injector well(s), may indicate that the gas injected during the huff period will travel more readily or more quickly from the respective injector well(s) to the respective offset well, thereby indicating that the artificial lift period for the offset well may be shorter than the huff period for the injector well (as shown in FIG. 11 ). Conversely, a lower interwell connectivity metric, indicative that there is less of a fluid connection between the respective offset well and the respective injector well(s), may indicate that the gas injected during the huff period will travel less readily or less quickly from the respective injector well(s) to the respective offset well, thereby indicating that the artificial lift period may be longer. In this regard, in one or some embodiments, the model(s) may determine both the timing of the respective stages and the lengths of times for the respective stages based on injection at one or more injector wells and/or based on the interwell connectivity metric for the one or more injector wells with the one or more offset wells.

As discussed above, one or more offset wells may be plugged during huffing, such as during huff 1 1060, huff 2 1070, and/or huff 3 1080. In one or some embodiments, the model(s) may determine which of the one or more offset wells to be plugged, such as based on the interwell connectivity metric. Merely by way of example, based on the interwell connectivity metric between a respective well (selected as an injector) and an offset well (e.g., the interwell connectivity metric indicates that injection of gas into the respective injector well will leak upward through the tubing of the offset well), the model(s) may determine which offset wells to plug. In effect, the proposed injector well communicates strongly (from a fluid standpoint) with a respective offset well so that a significant part (e.g., at least 30%; at least 40%; at least 50%; at least 60%; at least 70%; at least 80%; at least 90%) will flow to the respective offset well and be produced back. As such, plugging the offset well(s) is one way in which to contain the gas injected into the tubing. Under such circumstances, the respective offset well may be temporarily plugged. Conversely, in the event that the interwell connectivity metric between a proposed injector well and a proposed offset well is low such that the injected gas will not be produced back through the proposed offset well (less than 20% of injected fluid is produced back through the proposed offset well; less than 10%; less than 5%), the model may recommend not to plug the proposed offset well.

Also, the model(s) may determine the length of time to plug the one or more offset wells. As discussed above, plugging a well results in no hydrocarbon being extracted. As such, the model(s) are configured to weigh the costs of delaying extraction of hydrocarbon versus the possibility that injected gas will be produced via the offset wells. In particular, in one or some embodiments, the length of time to plug the one or more offset wells is identical to the time period of the huff stage (e.g., the length of time for huff 1 1060 is coextensive to and the same as the length of time for plugging a respective offset well). Alternatively, the length of time to plug the one or more offset wells is different than the time period of the huff stage. For example, in one or some embodiments, the length of time to plug a respective offset well may be less than the length of time for the huff stage.

In particular, huff 1 1060 may begin at t=X and end at t=Y. In one embodiment, the offset well may be plugged from t=X to t=Y (being coextensive and identical to huff 1 1060). Alternatively, the offset well may be plugged from t=X+Z to t=Y (being plugged later in time than the start of huff 1 1060, less than the total time period of huff 1 1060, but at least partly overlapping with the time period of huff 1 1060). Still alternatively, the offset well may be plugged from t=X+Z to t=Y+Z (being the same length as the time period of huff 1 1060, and at least partly overlapping with the time period of huff 1 1060). Yet alternatively, the offset well may be plugged from t=X+Z to t=Y+W, with W being less than Z (being a shorter length than the time period of huff 1 1060, but at least partly overlapping with the time period of huff 1 1060). Still yet alternatively, the offset well may be plugged from t=X+Z to t=Y+W, with W being greater than Z (being a longer length than the time period of huff 1 1060, and at least partly overlapping with the time period of huff 1 1060). Thus, in one or some embodiments, the model(s) may determine, such as based on the interwell connectivity metric(s), the length of the time in which the offset well is plugged and when the plug is inserted into the offset well relative to the huff for the injector well.

Further, similar to FIGS. 10-11 , the model(s) may determine the sequence of the stages of natural flow and artificial lift, and/or the length of time for the respective stages. For example, immediately after unplugging the offset well, the offset well may undergo a natural flow stage, following by an artificial lift stage. Though not illustrated in FIGS. 10-11 , the offset wells that are plugged do not produce hydrocarbons while plugged, but generally produce hydrocarbons when unplugged.

Thus, in determining the values of the parameters (e.g., the length and/or timing of the huff period and/or the length and/or timing of the artificial lift period) illustrated in FIGS. 10-11 , the models may consider may consider one or more time lags, including any one, any combination, or all of: a time delay indicative of: (1) time delay indicative of a shift in the effect of an input on the system's output dynamic response; or (2) time shift used to determine improved or optimal timing for gas lift.

With regard to (1), the time delay r may be expressed as a time shift in the input (e.g., control) variable(s), such as gas injection rate (q_(inj)). Merely by way of example, one manifestation of the time lag for (1) is illustrated in FIG. 6 as Δt (see resulting in Δt₁ and resulting in Δt₂) which may measure the lag in an offset well responsive to a pressure change in the injection well. In this regard, the modeling may identify the time discrepancy between system stimulus (e.g., the huff phase) and system response (e.g., the puff phase), in turn allowing for more accurate modeling of production phase, such as in cycles 1, 2, and 3.

In this regard, the response lag may be indicative of a time delay from injecting gas into the rock and the effect of the injection manifested in the pressure response in the offset wells (see, e.g., FIG. 6 ). In other words, the lag may be due to the reservoir's delayed response to gas injection.

For (1), there may be any one, any combination, or all of the following three components: (a) delay of pressure response to injection; (b) delay to unsoldered temporal components; or (c) time it takes fluids to transport between wells.

As discussed above, various equations such as Equations (4)-(10), may relate to the response lag. In particular, modeling (c) may include Equations (8)-(9). Further, modeling both (a) and (b) may be included in the time delay/lag (see τ in the Equations above). In this regard, the delay for (1) may be a function of any one, any combination, or all of: rock properties; location of the offset wells relative to injector well; chemistry of the injected gas (e.g., rich vs. lean gas); or fluid properties.

With regard to (2), the time shift may be needed to determine an improved/optimal timing for gas lift may be reflected in an expanded system models beyond Equations (4)-(10). In this way, the time shift may be used in order to determine the delay of the gas lift in the well (e.g., until the gas lift is needed). This is illustrated, for example, in FIG. 11 . In particular, FIG. 11 is for control of an offset well. Huff 1 indicates that an injector well is injected with gas. The offset well (shown in FIG. 11 ) begins cycle 1 with an artificial lift for a length of time based on the delayed effect of the huff (e.g., the delay in the gas injected in the injected well affecting the offset well).

As discussed above, FIG. 12 is a graph 1200 of hydrocarbon extraction from both injector well(s) and offset well(s) in the various stages, with 1220, 1222, 1224, 1226, 1240, 1242, 1244 representing the sum total of hydrocarbon extraction in the respective stages. In particular, hydrocarbon extraction from all of the wells including during the primary depletion stage is shown by curve 1220. Further, curves 1222, 1224, 1226, 1240, 1242, 1244 represent hydrocarbon extraction for all of the wells in the various cycles. In particular, as discussed above, certain wells, including the injector wells and the plugged offset wells, do not produce during the huff phase. As such, the hydrocarbon extraction is different, and typically lower, during the huff phase than during the puff phase. This is illustrated by the hydrocarbon extraction curves during the respective huff phases and puff phases (e.g., huff 1 1060 in which gas 1050 is injected resulting in curve 1040; puff 1 1062 resulting in curve 1222; huff 2 1070 in which gas 1052 is injected resulting in curve 1042; puff 2 1072 resulting in curve 1224; huff 3 1080 in which gas 1054 is injected resulting in curve 1044; puff 3 1082 resulting in curve 1226).

Further, FIG. 12 shows maximum oil rate constraint (e.g., capacity), illustrated as line 1210, which indicates a maximum amount of hydrocarbon that can be extracted. Maximum oil rate constraint is one example of a constraint to the system. Other constraints are contemplated. In one embodiment, the maximum oil rate constraint is set by an operator and input into the system. Alternatively, the design model 1020 may select the maximum oil rate constraint and/or other constraints from a set of possible values. After the constraint is set, the subsequent operation during the various phases of hydrocarbon extraction conform to the constraint. By way of example, the system may choke back production and/or reduce or eliminate gas injection in order to operate within the defined constraints.

Thus, as shown in FIG. 12 , the production, as illustrated by curves 1220, 1222, 1224, 1226, 1240, 1242, 1244 do not exceed the maximum oil rate constraint at any time. Further, as shown in FIG. 12 , the maximum oil rate constraint is approached or reached during the primary depletion stage and during cycle 3. In this regard, in one or some embodiments, the parameters selected for huffing in the cycles results in increase hydrocarbon extraction in subsequent or later cycles (e.g., the peak of curve 1224 is greater than the peak of curve 1222; the peak of curve 1226 is greater than the peak of curve 1224). Alternatively, the parameters selected for huffing in the cycles results in constant or near-constant hydrocarbon extraction in subsequent or later cycles. Still alternatively, the parameters selected for huffing in the cycles results in a decrease hydrocarbon extraction in subsequent or later cycles.

FIG. 12 illustrates a single huff and puff in a respective cycle, which may be determined by the model(s). This may be used for a single injector well or for multiple injector wells. For example, in one embodiment, only one injector well is selected for a respective huff stage, with the model(s) determining for the single injector well any one, any combination, or all of: timing of injection; length of time; maximum rate of injection; rate of increase/decrease of injection; type of gas injected; etc. Alternatively, the model(s) may select a plurality of injector wells (e.g., at least two injector wells; at least two injector wells; at least three injector wells; at least four injector wells; at least five injector wells; at least six injector wells; at least seven injector wells; at least eight injector wells; at least nine injector wells; etc.). Further, the model(s) may determine the parameters for injection in the plurality of injector wells, such as any one, any combination, or all of: timing of injection; length of time; maximum rate of injection; rate of increase/decrease of injection; type of gas injected; etc. In one embodiment, all of the parameters selected for huffing for the two or more of the different wells are identical. Alternatively, all of the parameters selected for two or more of the different wells are different. Still alternatively, two or more of the different wells may differ in one or more aspects and may be the same in a remainder of the aspects. In such an instance, the model(s), in order to improve or optimize the use of the injected gas for huffing, may determine for the different injector wells, any one, any combination, or all of:

-   -   the same or different sequences of injection at different         injection wells including any one, any combination, or all of:         start time of injection (e.g., start time of injection may be         the same or different at the different injection wells); end         time of injection (e.g., end time of injection may be the same         or different at the different injection wells); time length of         injection (e.g., the same time length of injection at the         different injection wells; different time lengths of injection         at the different injection wells); whether the injections at the         different wells at least partly overlap in time (e.g., the         injections at the different wells at least partly overlap in         time (such that they are coextensive); the injections at the         different wells do not overlap at all in time);     -   the same type or different types of gas injected in the         different injection wells;     -   the same volume or different volumes injected in the different         injection wells; or     -   the same rate or different rates of gas injection in the         different injection wells.

Further, the model(s) may determine for a respective cycle to perform at least one artificial lift (see FIGS. 10-11 ). Thus, in one embodiment, the model may recommend artificial lift for only one well in a respective cycle, and may select one, some or all of the following parameters for the artificial lift: timing of artificial lift; length of time of artificial lift; maximum rate of injection of artificial lift; rate of increase/decrease of artificial lift; type of gas injected; etc.

Alternatively, the model may recommend artificial lift for a plurality of wells (such as at least two wells, at least three wells, at least four wells; etc.) in a respective cycle, and may select for each respective well one, some or all of the following parameters for the artificial lift: timing of artificial lift; length of time of artificial lift; maximum rate of injection for artificial lift; rate of increase/decrease of artificial lift; type of gas injected; etc. In one embodiment, all of the parameters selected for artificial lift for two or more of the different wells are identical. Alternatively, all of the parameters selected for two or more of the different wells are different. Still alternatively, two or more of the different wells may differ in one or more aspects and may be the same in a remainder of the aspects. In such an instance, the model(s), in order to improve or optimize the use of the injected gas for artificial lift, may determine for the different wells, any one, any combination, or all of:

-   -   the same or different sequences of artificial lift at different         wells including any one, any combination, or all of: start time         of artificial lift (e.g., start time of artificial lift may be         the same or different at the different wells); end time of         artificial lift (e.g., end time of artificial lift may be the         same or different at the different wells); time length of         artificial lift (e.g., the same time length of artificial lift         at the different wells; different time lengths of artificial         lift at the different wells); whether the artificial lift at the         different wells at least partly overlap in time (e.g., the         artificial lift at the different wells at least partly overlap         in time (such that they are coextensive); the artificial lift at         the different wells do not overlap at all in time);     -   the same type or different types of gas used for artificial lift         in the different wells;     -   the same volume or different volumes of gas used for artificial         lift in the different wells; or     -   the same rate or different rates for artificial lift in the         different wells.

In addition, in one or some embodiments, the model(s) may determine for a respective cycle to include one artificial lift (see FIG. 10 ) or multiple artificial lifts (see FIG. 11 ). In the instance where multiple artificial lifts are included in a single cycle (see 1110, 1140), in one embodiment, the model(s) may select all of the parameters for each artificial lift within the single cycle to be identical.

It is noted that artificial lift 1110 may modify the pressure differential between the bottomhole and the wellhead for the offset well. In particular, there may be a lag τ in the effect of injecting gas into the reservoir since it may take time to build the pressure in the reservoir to a sufficient level to measure the impact on the production well. In this way, the lag τ may comprise the time period when the reservoir is affected by the gas injection sufficient to affect hydrocarbon production. In one or some embodiments, the interwell connectivity model may be used to determine a length of the lag τ (e.g., the length of time to achieve the desired reservoir pressure), and in turn, the length of the gas lift in order to compensate for the lag τ (see artificial lift). Though, it is noted that artificial lift 1110 may not necessarily be needed at the beginning of each respective cycle. In one or some embodiments, the lag τ may be determined by solving an objective function to obtain a value or a range for the lag τ. In turn, the solution for the lag τ may improve through model calibration.

Alternatively, the model(s) may select all of the parameters for each artificial lift within the single cycle for a single well to be different. Still alternatively, the two or more artificial lifts within a single cycle for a single well may differ in one or more aspects and may be the same in a remainder of the aspects. In such an instance, the model(s), in order to improve or optimize the use of the injected gas for artificial lifts within a single cycle for a single well, may determine any one, any combination, or all of:

-   -   the same or different sequences of artificial lift for the         single well in the respective cycle including any one, any         combination, or all of: time length of artificial lifts (e.g.,         the same time length of artificial lifts; different time lengths         of artificial lifts);     -   the same type or different types of gas used for the artificial         lifts for the single well in the respective cycle;     -   the same volume or different volumes of gas used for the         artificial lifts for the single well in the respective cycle; or     -   the same rate or different rates for the artificial lifts for         the single well in the respective cycle.

Similarly, the model(s) may recommend artificial lifts for a respective well in different cycles. See 1066, 1076, 1086 in FIG. 10 .

FIG. 14A is a block diagram 1400 of the system design for the multiple optimization models. As shown, one or more system models (such as system model 1 1420, etc.) may interact with one or more optimizations (e.g., design optimization 1410, annual plan optimization 1412, cycle operation optimization 1414, daily operation optimization 1416) and one or more update modules (e.g., update module 1430). Further, the stimulus (e.g., the input) may be input to physical system 1440 (which may represent various physical aspects of the system, such as any one, any combination, or all of: pads, facilities, compressor(s), reservoir(s), or well(s)).

In one or some embodiments, system model 1 1420 may comprise a model of one or more aspects of the system. For example, the system may include various parts for the surface, with one or more surface models associated with the various parts. In particular, the system may comprise a section from the wells to the manifold, from the manifold to the producing facility, one or more compressors, and the like. In this way, the surface model(s) may be associated with various operations on the surface, such as flow between well heads, gas compressors, dehydrators, etc. The system model may comprise a combination of surface model(s), gas lift model(s) (e.g., describing the flow from the surface to the bottomhole via the annulus of wells), and subsurface models (e.g., an interwell connectivity model that describes flow near injectors and between injector and offset wells during gas injection (huff) and production (puff)). Thus, the system model may comprise one or more models, which integrate the interwell connectivity model with the model of the one or aspects of the system, enabling prediction of the response of the system to various inputs (e.g., injecting gas in a particular well in the system).

As discussed above, design optimization 1410 may comprise design model 1020 and may determine one or more parameters regarding the development of the field (e.g., (1) the number of wells for drilling; (2) the spacing between the wells drilled; (3) the well design parameters (4) the specifics of completions; etc.). Further, the annual plan optimization 1412 may comprise annual planning model 1022 and may determine one or more parameters for an upcoming year of operation. Cycle operation optimization 1414 may comprise one or both of cycle operations model_1 1024 or cycle operations model_1 1026 and may determine one or more parameters for a respective cycle of operations. A model for daily operations optimization 1416 may comprise any one, any combination, or all of daily operations model 1030, daily operations model 1032, or daily operations model 1034 and may determine one or more parameters for daily operations with a respective cycle.

As discussed above, the optimization model(s) may comprise flow model(s) that optionally constrains one or more individual components (e.g., any one, any combination, or all of gas lift gas rate, compression capacity, flow capacity imposed by choke set points at wellheads, etc.). In one or some embodiments, optimization controls and objectives may be different for each optimization model. By way of example, the cycle operation optimization 1414 may focus on optimizing oil production within a respective cycle, and determine the controls for various operations, such as, for example, gas injection volume. Likewise, the daily operation optimization 1416 may focus on optimizing oil production within on a daily basis, and determine the controls for various operations within a respective day, such as, for example, choke or gas lift rate. In contrast, annual plan optimization 1412 may focus on longer term strategic planning across multiple cycles (e.g., how much gas volume is needed within a respective year; how large of a compressor is needed for the respective year). Thus, using the various optimization models, optimization may be performed in presence of uncertainty (e.g., uncertainty associated with parameters V, a, b etc., with optimization performed by analyzing different scenarios of the parameters).

FIG. 14B is a block diagram of inputs to and outputs from the analytical (predictive) model 1450. As shown in FIG. 14B, any one, any combination, or all of the following may be input to analytical (predictive) model 1450: control input(s) (e.g., control(s) from system model 1420); data input(s) (e.g., data related to the gas injection, such as any one, any combination, or all of: injection rate (e.g., daily injection rate); injection period; or type of injected gas (μ)); input(s) regarding production system design parameters (e.g., one or more outputs from Design Optimization 1410); or input(s) regarding reservoir parameters.

In one or some embodiments, the data input(s), such as the data related to gas injection, may be generated from one or more optimization models including any one, any combination, or all of: annual plan optimization 1412, cycle operation optimization 1414, or daily operation optimization 1416. In one or some embodiments, the input(s) regarding production system design parameters may comprise any one, any combination, or all of: number of wells; well placement; well survey; pipeline topology; number of compressors; or size of compressors. In one or some embodiments, the input(s) regarding reservoir parameters include any one, any combination, or all of: reservoir parameters themselves; well connectivity (e.g., a, b); or volumes (V1, V2, V3), which may be from Model Update Module 1430. Alternatively, or in addition, the input(s) regarding reservoir parameters may comprise one or both of reservoir fluids or PVT data.

As shown in FIG. 14B, the analytical (predictive) model 1450 may generate one or more outputs, such as one or both of outputs relating to production (e.g., production rates) or one or more physical effects due to gas injected in the subsurface (e.g., reservoir pressure). Further, the pressure, such as reservoir pressure, may be in one of several forms. In one form, the reservoir pressure may comprise a distribution (e.g., dependent on location in the subsurface). For example, pressure in the vicinity of a hydraulic fracture may comprise a distribution. As discussed above, the model may generate the pressure in the vicinity of the hydraulic fracture, such as in the planes at or near the hydraulic fractures. See V1, V2, V3 discussed above. Alternatively, or in addition, the model may determine the pressure (such as the average pressure) in the volume of the reservoir. As such, the model may determine the pressure differential between various parts of the subsurface, such as from the reservoir to one or more other parts (e.g., the bottomhole(s)).

Further, as discussed above with regard to FIGS. 8A-C, the fluid communication between the wells may depend on the type of fractures. For example, if there is an offset well that has fractures that communicate with the fractures of the injector well (e.g., an overlap, such as illustrated in FIGS. 8A and 8C), displacement will occur (e.g., injected gas from an injector well may push oil into the offset well). If the fractures are disconnected (see FIG. 8B in which the fractures do not overlap), an injector well, previously injecting gas, may thereafter produce hydrocarbons (with the injected gas).

FIG. 15 is flow diagram 1500 for optimization in one or more stages, including the design stage and the huff and puff stage. At 1502, initial point(s), such as initial values, are accessed. At 1504, a global search is performed, including discrete variables, using a low-fidelity model. At 1506, the methodology determines whether a new optimum has been found. If not, flow diagram 1500 loops back to 1504. If so, flow diagram 1500 goes to 1508, in which a local search is performed using a high-fidelity model. At 1510, the methodology again determines whether a new optimum has been found. If not, flow diagram 1500 loops back to 1504. If so, flow diagram 1500 goes to 1512, in which the local search is refined. At 1514, the methodology determines whether stopping criteria have been met. Various stopping criteria are contemplated, such as depending on whether results of the local search are within certain predefined values. If not, flow diagram 1500 loops back to 1504. If so, flow diagram 1500 ends.

FIG. 16 is a flow diagram 1600 for optimization, accounting for uncertainty using conditional value-at-risk (CVaR) net present value (NPV). At 1602, initialization is performed. For example, one or more sets of variables, such as one or both of continuous or discrete variables are initialized. In one or some embodiments, the optimum values of the variables are not known. Prior to iterating, an initial value is selected.

At 1604, it is determined whether to perform optimization of discrete variables. In particular, optimization of discrete variables may be performed in one of several ways. In one way, a potentially non-linear objective function may be simplified, such as by substituting a piecewise linear function, which may provide an estimate for the discrete variables. After which, the piecewise linear function may be examined for error, and iteratively modified until the error is less than a predetermined value.

Further, if optimization of the discrete variables is not to be performed, at 1606, sweeping for discrete variables is performed. For example, the solution space may be reduced by eliminating infeasible solutions, with the user sweeping a specific area of the solution space to select the values for the discrete variables.

Further, it may be determined to optimize the continuous variables. If so, at 1608, optimization is performed, thereafter at 1610, function calculation is performed, and thereafter at 1612, a HnP simulation model is run to calculate the conditional value at risk (CVaR) net present value (NPV). Through the loop of 1608, 1610, 1612, it may be determined whether to continue iterating to optimize the values selected for the continuous variables. Thus, in one or some embodiments, optimization of both the discrete variables and the continuous variables may be performed at the same time.

If at 1604, it is determined that the optimization of discrete variables has been performed, at 1614, it is determined whether the best discrete variables are integer. If so, flow diagram 1600 ends. If not, at 1616, a new sub-problem is created, and flow diagram 1600 iterates back to 1602 to initialize.

FIG. 17 is a representation 1700 of an injector well 1740, an offset well 1710, and the reservoir 1750. Fluid 1770, such as water, gas, etc. is injected via the wellhead 1742 of injector well 1740, with the fluid 1770 flowing as shown at arrow 1772 into reservoir. Injection may change pressure in various parts of the system, such as pressure at the bottomhole 1744 for the injector well (P_(b,i)), pressure in the reservoir (P_(r)), and pressure at the bottomhole 1714 for the offset well (P_(b,o)). Further, pressure differentials may be calculated, such as ΔP₁ 1760, which is the difference between pressure in the reservoir (P_(r)) and pressure at the bottomhole 1714 for the offset well (P_(b,o)), and ΔP₂ 1762, which is the difference between pressure at the bottomhole 1714 for the offset well (P_(b,o)) and pressure at the wellhead 1712 (which may be affected by gas lift 1780 such as creating a pressure differential such that fluid from the bottomhole 1714 is guided upward to wellhead 1712. ΔP₁ 1760 is an example of the inflow performance relationship, which may comprise an indicator for pressure differential from the reservoir to a part of the well, such as the wellbore.

As discussed above, control of gas injected into the reservoir may create predetermined pressure in one or more parts of the subsurface, such as predetermined pressure differentials between different parts of the subsurface (e.g., between the reservoir and one or more bottomholes). Thus, via gas injection into the subsurface, a predetermined pressure profile (and predetermined pressure gradient(s)) in the subsurface may be created. Further, control of gas lift may create a predetermined pressure differential within a respective well (e.g., between the bottomhole and the wellhead of the respective well). In this way, a predetermined pressure path, with one or more predetermined pressure gradients, may be created from the reservoir to the wellhead. As discussed previously, the interwell connectivity model may be used to manage the injection of gas into the subsurface and may be used to determine whether (or when) to perform the gas lift.

Thus, when injecting gas near or proximate to the reservoir, pressure increases in the reservoir, creating the requisite pressure differential. Further, gas lift within a nearby well (whether in an offset well during and after gas injection and/or in an injector well after gas injection) may be performed to complement or be in concert with the created pressure differential in the subsurface in order to guide the flow of hydrocarbons from the reservoir to the wellhead. Further, the gas lift for a respective well may be performed in a selective or an optimized manner dependent on one or more factors, such as the amount of hydrocarbons flowing in the respective well and/or the pressure differential within the subsurface. In this way, the gas lift, which its attendant costs, may be performed only when needed.

In particular, unlike a process that may simultaneously inject gas into the reservoir and into the annulus (for gas lift), the disclosed methodology may be used to determine whether, and when, to perform one of the gas processes (e.g., one of the gas injection into the reservoir or gas lift), to perform both of the gas processes (e.g., both of the gas injection into the reservoir or gas lift), or to perform neither of the gas processes, in an effort to coordinate the gas injection and/or gas lift to get the hydrocarbons from the reservoir to the surface. This is illustrated above, for example, with regard to FIGS. 10-12 , in which different sequences of gas injection and/or gas lift are performed in a coordinated manner.

In this way, the interwell connectivity model may be used in a variety of contexts, such as a predictive model (e.g., certain set of inputs generates a certain set of outputs, or vice-versa, such as illustrated in FIG. 14B) and/or a prescriptive model (e.g., an optimization model that selects one or more values to optimize based on pre-defined metrics). For example, with regard to the prescriptive model, optimization may be performed in one of several ways, including: (i) determine, from a manually generated set of potential values, the optimal set of values; and/or (ii) determine, from an automatic search in decision space indicative of different sets of potential values, the optimal set of values. In this regard, the interwell connectivity model allows for an understanding of the effect of gas injection without undue computer processing requirements.

Further, the flow in various parts of the subsurface may be represented in one of several ways. For example, the flow in the reservoir (e.g., from reservoir 1750 to offset well 1710) may be represented in equation form (e.g., see equations (17)-(18) above), in model form, or via reservoir simulation. As another example, the flow within a well (e.g., within offset well 1710) may be represented by a hydraulic model. In this regard, one or more models (one or more of which may be based on the interwell connectivity metric) may be used to indicate the flow of fluid in various parts of the subsurface.

In all practical applications, the present technological advancement must be used in conjunction with a computer, programmed in accordance with the disclosures herein. For example, FIG. 18 is a diagram of an exemplary computer system 1800 that may be utilized to implement methods described herein. A central processing unit (CPU) 1802 is coupled to system bus 1804. The CPU 1802 may be any general-purpose CPU, although other types of architectures of CPU 1802 (or other components of exemplary computer system 1800) may be used as long as CPU 1802 (and other components of computer system 1800) supports the operations as described herein. Those of ordinary skill in the art will appreciate that, while only a single CPU 1802 is shown in FIG. 18 , additional CPUs may be present. Moreover, the computer system 1800 may comprise a networked, multi-processor computer system that may include a hybrid parallel CPU/GPU system. The CPU 1802 may execute the various logical instructions according to various teachings disclosed herein. For example, the CPU 1802 may execute machine-level instructions for performing processing according to the operational flow described.

The computer system 1800 may also include computer components such as non-transitory, computer-readable media. Examples of computer-readable media include computer-readable non-transitory storage media, such as a random-access memory (RAM) 1806, which may be SRAM, DRAM, SDRAM, or the like. The computer system 1800 may also include additional non-transitory, computer-readable storage media such as a read-only memory (ROM) 1808, which may be PROM, EPROM, EEPROM, or the like. RAM 1806 and ROM 1808 hold user and system data and programs, as is known in the art. The computer system 1800 may also include an input/output (I/O) adapter 1810, a graphics processing unit (GPU) 1814, a communications adapter 1822, a user interface adapter 1824, a display driver 1816, and a display adapter 1818.

The I/O adapter 1810 may connect additional non-transitory, computer-readable media such as storage device(s) 1812, including, for example, a hard drive, a compact disc (CD) drive, a floppy disk drive, a tape drive, and the like to computer system 1800. The storage device(s) may be used when RAM 1806 is insufficient for the memory requirements associated with storing data for operations of the present techniques. The data storage of the computer system 1800 may be used for storing information and/or other data used or generated as disclosed herein. For example, storage device(s) 1812 may be used to store configuration information or additional plug-ins in accordance with the present techniques. Further, user interface adapter 1824 couples user input devices, such as a keyboard 1828, a pointing device 1826 and/or output devices to the computer system 1800. The display adapter 1818 is driven by the CPU 1802 to control the display on a display device 1820 to, for example, present information to the user such as subsurface images generated according to methods described herein.

The architecture of computer system 1800 may be varied as desired. For example, any suitable processor-based device may be used, including without limitation personal computers, laptop computers, computer workstations, and multi-processor servers. Moreover, the present technological advancement may be implemented on application specific integrated circuits (ASICs) or very large scale integrated (VLSI) circuits. In fact, persons of ordinary skill in the art may use any number of suitable hardware structures capable of executing logical operations according to the present technological advancement. The term “processing circuit” encompasses a hardware processor (such as those found in the hardware devices noted above), ASICs, and VLSI circuits. Input data to the computer system 1800 may include various plug-ins and library files. Input data may additionally include configuration information.

Preferably, the computer is a high-performance computer (HPC), known to those skilled in the art. Such high-performance computers typically involve clusters of nodes, each node having multiple CPU's and computer memory that allow parallel computation. The models may be visualized and edited using any interactive visualization programs and associated hardware, such as monitors and projectors. The architecture of system may vary and may be composed of any number of suitable hardware structures capable of executing logical operations and displaying the output according to the present technological advancement. Those of ordinary skill in the art are aware of suitable supercomputers available from Cray or IBM or other cloud computing based vendors such as Microsoft, Amazon.

The above-described techniques, and/or systems implementing such techniques, can further include hydrocarbon management based at least in part upon the above techniques, including using the AI model in one or more aspects of hydrocarbon management. For instance, methods according to various embodiments may include managing hydrocarbons based at least in part upon the one or more generated AI models and data representations constructed according to the above-described methods. In particular, such methods may include performing various welds in the context of drilling a well, and/or causing a well to be drilled, based at least in part upon the one or more generated geological models and data representations discussed herein (e.g., such that the well is located based at least in part upon a location determined from the models and/or data representations, which location may optionally be informed by other inputs, data, and/or analyses, as well) and further prospecting for and/or producing hydrocarbons using the well.

It is intended that the foregoing detailed description be understood as an illustration of selected forms that the invention can take and not as a definition of the invention. It is only the following claims, including all equivalents which are intended to define the scope of the claimed invention. Further, it should be noted that any aspect of any of the preferred embodiments described herein may be used alone or in combination with one another. Finally, persons skilled in the art will readily recognize that in preferred implementation, some, or all of the steps in the disclosed method are performed using a computer so that the methodology is computer implemented. In such cases, the resulting physical properties model may be downloaded or saved to computer storage.

The following example embodiments of the invention are also disclosed.

Embodiment 1: A computer-implemented method for enhanced oil recovery (EOR) for a plurality of wells in one or more intervals, the method comprising:

-   -   accessing an interwell connectivity model comprising interwell         connectivity metrics indicative of fluid interconnectivity         amongst at least pairs of wells in the plurality of wells, the         interwell connectivity model including controllable one or more         inputs for inputting gas into a reservoir and one or more         outputs related to EOR; and controlling, based on the interwell         connectivity model, the one or more inputs for EOR.

Embodiment 2: The method of embodiment 1,

-   -   wherein the interwell connectivity model is used to determine         pressure in a reservoir of a subsurface; and     -   wherein the one or more inputs for EOR comprise one or more         inputs related to injection of gas.

Embodiment 3: The method of any of embodiments 1 or 2,

-   -   wherein the interwell connectivity model is used to determine         the pressure in the reservoir of the subsurface based on one or         both of an amount of the gas injected into the reservoir or a         time period of injecting the gas into the reservoir.

Embodiment 4: The method of any of embodiments 1-3,

-   -   wherein the interwell connectivity model is used to determine         average pressure in the reservoir of the subsurface.

Embodiment 5: The method of any of embodiments 1-4,

-   -   wherein the interwell connectivity metrics correlate the         pressure to fluid transport between two or more wells.

Embodiment 6: The method of any of embodiments 1-5,

-   -   wherein the interwell connectivity metric correlates the fluid         transport to an exponential of an average pressure between the         two or more wells.

Embodiment 7: The method of any of embodiments 1-6,

-   -   wherein the interwell connectivity model is used to determine,         when injecting gas into the reservoir, pressure differentials         between the reservoir and one or more bottomholes for EOR of         hydrocarbons in the reservoir.

Embodiment 8: The method of any of embodiments 1-7,

-   -   further comprising performing at least one huff and at least one         puff, the at least one huff comprises injecting the gas in the         reservoir, the at least one puff comprises, after injecting the         gas in the reservoir, not injecting the gas in the reservoir;     -   wherein the interwell connectivity model is used to determine at         least one effect from performing the at least one huff, the at         least one effect comprising one or both of: (i) a change in         pressure in at least a part of the reservoir, in one or more         injector wells, or in one or more offset wells (ii) a change in         production rates; and     -   wherein the interwell connectivity model is used to determine at         least one effect from performing the at least one puff, the at         least one effect comprising one or both of: (i) the change in         pressure in the at least a part of the reservoir, in the one or         more injector wells, or in the one or more offset wells; or (ii)         the change in production rates.

Embodiment 9: The method of any of embodiments 1-8

-   -   further comprising:         -   performing at least one huff and at least one puff, the at             least one huff comprises injecting the gas in the reservoir,             the at least one puff comprises, after injecting the gas in             the reservoir, not injecting the gas in the reservoir; and         -   performing at least one gas lift in which gas is injected             into an annulus of one or more wells; and     -   wherein the interwell connectivity model is used to coordinate         performing the at least one huff and the at least one puff with         the at least one gas lift in order to create a pressure         differential in order to extract hydrocarbon from the reservoir         through the one or more wells.

Embodiment 10: The method of any of embodiments 1-9

-   -   wherein the at least one huff increases the pressure         differential between the reservoir and bottomholes in the one or         more wells;     -   wherein the at least one gas lift increases the pressure         differential between the bottomholes and wellhead in the one or         more wells; and     -   wherein the interwell connectivity model is used to coordinate         the increases in the pressure differentials between the         reservoir and bottomholes in the one or more wells and between         the bottomholes and the wellhead in the one or more wells in         order to extract the hydrocarbon through the one or more wells.

Embodiment 11: The method of any of embodiments 1-10,

-   -   wherein during the at least one huff, the gas is injected into         the reservoir via one or more injector wells and the         hydrocarbons are extracted via one or more offset wells; and     -   wherein the interwell connectivity model is used for determining         to perform the at least one gas lift on the one or more offset         wells while performing the at least one huff on the one or more         injector wells.

Embodiment 12: The method of any of embodiments 1-11,

-   -   wherein the interwell connectivity model is used for determining         to perform the at least one gas lift on one or both of the one         or more offset wells or the one or more injector wells while         performing the at least one puff.

Embodiment 13: The method of any of embodiments 1-12,

-   -   wherein the fluid flow between the respective pairs of wells is         dependent on the interwell connectivity metrics assigned to the         respective pairs and pressures in the respective pairs of wells         and inversely dependent on viscosity of fluid injected into one         or more injector wells.

Embodiment 14: The method of any of embodiments 1-13,

-   -   wherein the one or more intervals includes an injector well and         neighboring wells;     -   wherein the neighboring wells include a first offset well and a         second offset well; and     -   wherein the interwell connectivity model predicts bottomhole         pressure (BHP) in the injector well as a function of a number         and configuration of neighboring wells and as a function of a         first interwell connectivity metric between the injector well         and the first offset well and a second interwell connectivity         metric between the injector well and the second offset well.

Embodiment 15: The method of any of embodiments 1-14,

-   -   wherein the interwell connectivity model predicts the bottomhole         pressure in at least the first offset well and the second offset         well.

Embodiment 16: The method of any of embodiments 1-15,

-   -   wherein the interwell connectivity model further predicts one or         both of oil recovery or oil uplift based on the predicted BHP.

Embodiment 17: The method of any of embodiments 1-16,

-   -   wherein the interwell connectivity model predicts compression         necessary to overwhelm well-to-well communication between the         injector well and the first offset well and between the injector         well and the second offset well as a function of pressure, fluid         properties of injected fluid, and layout or geometry of the         wells.

Embodiment 18: The method of any of embodiments 1-17,

-   -   wherein the interwell connectivity metrics are determined based         on a time lag for pressure to travel from an injector well to an         offset well.

Embodiment 19: The method of any of embodiments 1-18,

-   -   wherein the interwell connectivity metrics are hysteretic based         on the time lag as the pressure is building up and based on the         time lag as the pressure is drawing down.

Embodiment 20: The method of any of embodiments 1-19,

-   -   wherein the interwell connectivity metrics are not dependent on         a magnitude or percent pressure change in a given time interval.

Embodiment 21: The method of any of embodiments 1-20,

-   -   wherein the time lag is between a change in injection rate in         the injector well to when a sensed change in bottomhole pressure         in the offset well; and     -   wherein the interwell connectivity model is used as a fracture         diagnostic technique based on the time lag.

Embodiment 22: The method of any of embodiments 1-21,

-   -   wherein the time lag is indicative of a path of least resistance         between the injector well and the offset well; and     -   wherein the fracture diagnostic technique eliminates one or more         fracture scenarios inconsistent with interpreted interwell         connectivity.

Embodiment 23: The method of any of embodiments 1-22,

-   -   wherein the interwell connectivity model enables strength of         well-to-well interaction to change as a function of average         bottomhole pressure and whether pressure is building up or         drawing down, such that the interwell connectivity model is used         to characterize the well-to-well interactions by a plurality of         flow regimes.

Embodiment 24: The method of any of embodiments 1-23,

-   -   wherein the interwell connectivity model, which describes         interwell connectivity as a function of pressure, estimates an         amount of gas needed to build pressure as a function of         injection rate.

Embodiment 25: A non-transitory computer readable medium having stored thereon software instructions that, when executed by a processor, cause the processor to perform the method of any of embodiments 1-24.

Embodiment 26: A system comprising a processor and a memory, the processor in communication with the memory, the memory having stored thereon software instructions that, when executed by the processor, cause the processor to perform the method of any of embodiments 1-24.

Embodiment 27: A method for hydrocarbon extraction comprising:

-   -   accessing an interwell connectivity model that is indicative of         fluid connectivity of a plurality of wells;     -   determining, based on the interwell connectivity model, one or         more aspects of one or both of control or configuration of the         plurality of wells; and     -   using the one or more aspects of one or both of control or         configuration of the plurality of wells for hydrocarbon         management of a reservoir.

Embodiment 28 The method of embodiment 27,

-   -   wherein determining the one or more aspects of one or both of         control or configuration of the plurality of wells comprises         determining one or more aspects associated with one or both of a         drilling phase or a construction phase of hydrocarbon         management.

Embodiment 29: The method of any of embodiments 17 or 28,

-   -   wherein the one or more aspects associated with one or both of         the drilling phase or the construction phase of hydrocarbon         management comprise one or more of: a number of the plurality of         wells; a placement of the plurality of wells; fracturing         associated with the plurality of wells; or at least one of a         compressor for pumping regarding the wells or piping to the         wells.

Embodiment 30: The method of any of embodiments 27-29,

-   -   wherein determining the one or more aspects of one or both of         control or configuration of the plurality of wells comprises         determining one or more aspects associated with a primary         depletion phase of hydrocarbon management.

Embodiment 31: The method of any of embodiments 27-30,

-   -   wherein determining the one or more aspects associated with the         primary depletion phase of hydrocarbon management comprises         determining a time when to end primary depletion.

Embodiment 32: The method of any of embodiments 27-31,

-   -   wherein determining the one or more aspects of one or both of         control or configuration of the plurality of wells comprises         determining, based on the interwell connectivity model, one or         both of whether or when to begin injecting gas into at least one         of the plurality of wells.

Embodiment 33: The method of any of embodiments 27-32,

-   -   wherein the interwell connectivity model in combination with an         optimization model are used to determine whether to inject the         gas into tubing or into an annulus of one or more wells.

Embodiment 34: The method of any of embodiments 27-33,

-   -   wherein the plurality of wells comprises one or more injector         wells into which gas is injected into the tubing; and     -   wherein the interwell connectivity model in combination with the         optimization model determine whether to inject the gas into         tubing by analyzing a time delay of an effect of injecting the         gas into the one or more injector wells on one or more offset         wells.

Embodiment 35: The method of any of embodiments 27-34,

-   -   wherein the one or more injector wells comprises a first         injector well and a second injector well; and     -   wherein the interwell connectivity model in combination with the         optimization model are used to determine, based on the time         delay, one or both of a timing of injection of the gas into the         tubing based on the gas injected into the tubing of the first         injector well.

Embodiment 36: The method of any of embodiments 27-35,

-   -   wherein the plurality of wells comprises one or more injector         wells into which gas is injected into the tubing and one or more         offset wells in which gas is not injected into the tubing; and     -   wherein the interwell connectivity model in combination with the         optimization model are used to determine for the one or more         offset wells one or more aspects of injecting the gas into the         annulus of the one or more offset wells based on the gas         injected into the tubing of the one or more injector wells.

Embodiment 37: The method of any of embodiments 27-36,

-   -   wherein the interwell connectivity model in combination with the         optimization model are used to determine, based on a time delay         of an effect of injecting the gas into the tubing of the one or         more injector wells on the one or more offset wells, when to         inject the gas into the annulus of the one or more offset wells.

Embodiment 38: The method of any of embodiments 27-37,

-   -   wherein hydrocarbons are extracted from a subsurface via the one         or more offset wells;     -   wherein the effect of injecting the gas into the tubing of the         one or more injector wells comprises a mixing of the gas with         the hydrocarbons in the subsurface;     -   wherein the interwell connectivity model in combination with the         optimization model are used to determine when to begin injecting         gas into an annulus of the one or more offset wells based on the         time delay of the effect of injecting the gas into the tubing of         the one or more injector wells.

Embodiment 39: The method of any of embodiments 27-38,

-   -   further comprising, responsive to receiving production data,         updating one or more of parameters, bias or time delay of the         interwell connectivity model.

Embodiment 40: The method of any of embodiments 27-39,

-   -   wherein the time delay is indicative of an effect of injecting         gas into at least a part of a well; and     -   wherein updating the time delay of the interwell connectivity         model comprises using production data and data indicative of         previous injection of gas into the at least a part of the well.

Embodiment 41: The method of any of embodiments 27-40,

-   -   wherein hydrocarbon is extracted using a plurality of cycles of         injecting gas into the at least a part of the well; and     -   wherein the interwell connectivity model is updated based on the         production data and the data from a previous cycle of injecting         gas into the at least a part of the well.

Embodiment 42: The method of any of embodiments 27-41,

-   -   the interwell connectivity model includes: (i) discrete or         categorical variables; and (ii) continuous variables; and     -   wherein updating the interwell connectivity model includes         updating both the discrete or categorical variables and the         continuous variables.

Embodiment 43: The method of any of embodiments 27-42,

-   -   wherein the interwell connectivity model in combination with an         optimization model are used to determine when to begin injecting         gas or how much of the gas to inject into at least a part of the         reservoir.

Embodiment 44: The method of any of embodiments 27-43,

-   -   wherein the interwell connectivity model in combination with an         optimization model are used to determine in which one or more of         the plurality of wells to inject the gas into tubing of the one         or more of the plurality of wells in order to disperse gas in at         least a part of the reservoir.

Embodiment 45: The method of any of embodiments 27-44,

-   -   wherein the one or more of the plurality of wells comprise one         or more injector wells;     -   wherein one or more offset wells comprise one or more remainder         wells in which gas is not injected into the tubing of the one or         more offset wells; and     -   wherein operation of at least one aspect of the one or more         offset wells is performed based on injecting gas into the tubing         of the one or more injector wells.

Embodiment 46: The method of any of embodiments 27-45,

-   -   wherein artificial lift comprises injecting the gas in an         annulus;     -   wherein huffing comprises injecting the gas in the tubing; and     -   wherein one or more aspects of the artificial lift in the one or         more offset wells is determined based on the huffing in one or         more injector wells.

Embodiment 47: The method of any of embodiments 27-46,

-   -   wherein one or both of a time to stop injecting the gas into the         annulus of the one or more offset wells for the artificial lift         or a volume of the gas injected into the annulus for the         artificial lift is determined based on the injecting of gas into         the tubing of the one or more injector wells.

Embodiment 48: The method of any of embodiments 27-47,

-   -   wherein determining the one or more aspects of the artificial         lift based on the huffing in the one or more injector wells         comprises:     -   determining a migration of the gas through the tubing in the one         or more injector wells in the reservoir;     -   determining an effect of the migration of the gas in the         reservoir on the one or more offset wells; and     -   selecting, based on the effect of the migration of the gas in         the reservoir on the one or more offset wells, the one or more         aspects of the artificial lift in the one or more offset wells.

Embodiment 49: The method of any of embodiments 27-48,

-   -   wherein determining the one or more aspects of one or both of         control or configuration of the plurality of wells comprise         determining two or more cycles of: injecting one or more gases         into tubing of at least one of the plurality of wells; and         injecting the one or more gases into an annulus of one or more         of the plurality of wells.

Embodiment 50: The method of any of embodiments 27-49,

-   -   wherein the two or more cycles comprise:     -   injecting the one or more gases into the tubing of a plurality         of injector wells; and     -   injecting the one or more gases into the annulus of one or more         of the plurality of injector wells and one or more offset wells.

Embodiment 51: A non-transitory computer readable medium having stored thereon software instructions that, when executed by a processor, cause the processor to perform the method of any of embodiments 27-50.

Embodiment 52: A system comprising a processor and a memory, the processor in communication with the memory, the memory having stored thereon software instructions that, when executed by the processor, cause the processor to perform the method of any of embodiments 27-50. 

What is claimed is:
 1. A computer-implemented method for enhanced oil recovery (EOR) for a plurality of wells in one or more intervals, the method comprising: accessing an interwell connectivity model comprising interwell connectivity metrics indicative of fluid interconnectivity amongst at least pairs of wells in the plurality of wells, the interwell connectivity model including controllable one or more inputs for inputting gas into a reservoir and one or more outputs related to EOR; and controlling, based on the interwell connectivity model, the one or more inputs for EOR.
 2. The method of claim 1, wherein the interwell connectivity model is used to determine pressure in a reservoir of a subsurface; and wherein the one or more inputs for EOR comprise one or more inputs related to injection of gas.
 3. The method of claim 2, wherein the interwell connectivity model is used to determine the pressure in the reservoir of the subsurface based on one or both of an amount of the gas injected into the reservoir or a time period of injecting the gas into the reservoir.
 4. The method of claim 3, wherein the interwell connectivity model is used to determine average pressure in the reservoir of the subsurface.
 5. The method of claim 2, wherein the interwell connectivity metrics correlate the pressure to fluid transport between two or more wells.
 6. The method of claim 5, wherein the interwell connectivity metric correlates the fluid transport to an exponential of an average pressure between the two or more wells.
 7. The method of claim 2, wherein the interwell connectivity model is used to determine, when injecting gas into the reservoir, pressure differentials between the reservoir and one or more bottomholes for EOR of hydrocarbons in the reservoir.
 8. The method of claim 7, further comprising performing at least one huff and at least one puff, the at least one huff comprises injecting the gas in the reservoir, the at least one puff comprises, after injecting the gas in the reservoir, not injecting the gas in the reservoir; wherein the interwell connectivity model is used to determine at least one effect from performing the at least one huff, the at least one effect comprising one or both of: (i) a change in pressure in at least a part of the reservoir, in one or more injector wells, or in one or more offset wells (ii) a change in production rates; and wherein the interwell connectivity model is used to determine at least one effect from performing the at least one puff, the at least one effect comprising one or both of: (i) the change in pressure in the at least a part of the reservoir, in the one or more injector wells, or in the one or more offset wells; or (ii) the change in production rates.
 9. The method of claim 7, further comprising: performing at least one huff and at least one puff, the at least one huff comprises injecting the gas in the reservoir, the at least one puff comprises, after injecting the gas in the reservoir, not injecting the gas in the reservoir; and performing at least one gas lift in which gas is injected into an annulus of one or more wells; and wherein the interwell connectivity model is used to coordinate performing the at least one huff and the at least one puff with the at least one gas lift in order to create a pressure differential in order to extract hydrocarbon from the reservoir through the one or more wells.
 10. The method of claim 9, wherein the at least one huff increases the pressure differential between the reservoir and bottomholes in the one or more wells; wherein the at least one gas lift increases the pressure differential between the bottomholes and wellhead in the one or more wells; and wherein the interwell connectivity model is used to coordinate the increases in the pressure differentials between the reservoir and bottomholes in the one or more wells and between the bottomholes and the wellhead in the one or more wells in order to extract the hydrocarbon through the one or more wells.
 11. The method of claim 10, wherein during the at least one huff, the gas is injected into the reservoir via one or more injector wells and the hydrocarbons are extracted via one or more offset wells; and wherein the interwell connectivity model is used for determining to perform the at least one gas lift on the one or more offset wells while performing the at least one huff on the one or more injector wells.
 12. The method of claim 11, wherein the interwell connectivity model is used for determining to perform the at least one gas lift on one or both of the one or more offset wells or the one or more injector wells while performing the at least one puff.
 13. The method of claim 2, wherein the fluid flow between the respective pairs of wells is dependent on the interwell connectivity metrics assigned to the respective pairs and pressures in the respective pairs of wells and inversely dependent on viscosity of fluid injected into one or more injector wells.
 14. The method of claim 2, wherein the one or more intervals includes an injector well and neighboring wells; wherein the neighboring wells include a first offset well and a second offset well; and wherein the interwell connectivity model predicts bottomhole pressure (BHP) in the injector well as a function of a number and configuration of neighboring wells and as a function of a first interwell connectivity metric between the injector well and the first offset well and a second interwell connectivity metric between the injector well and the second offset well.
 15. The method of claim 14, wherein the interwell connectivity model predicts the bottomhole pressure in at least the first offset well and the second offset well.
 16. The method of claim 15, wherein the interwell connectivity model further predicts one or both of oil recovery or oil uplift based on the predicted BHP.
 17. The method of claim 16, wherein the interwell connectivity model predicts compression necessary to overwhelm well-to-well communication between the injector well and the first offset well and between the injector well and the second offset well as a function of pressure, fluid properties of injected fluid, and layout or geometry of the wells.
 18. The method of claim 1, wherein the interwell connectivity metrics are determined based on a time lag for pressure to travel from an injector well to an offset well.
 19. The method of claim 18, wherein the interwell connectivity metrics are hysteretic based on the time lag as the pressure is building up and based on the time lag as the pressure is drawing down.
 20. The method of claim 19, wherein the interwell connectivity metrics are not dependent on a magnitude or percent pressure change in a given time interval.
 21. The method of claim 18, wherein the time lag is between a change in injection rate in the injector well to when a sensed change in bottomhole pressure in the offset well; and wherein the interwell connectivity model is used as a fracture diagnostic technique based on the time lag.
 22. The method of claim 21, wherein the time lag is indicative of a path of least resistance between the injector well and the offset well; and wherein the fracture diagnostic technique eliminates one or more fracture scenarios inconsistent with interpreted interwell connectivity.
 23. The method of claim 1, wherein the interwell connectivity model enables strength of well-to-well interaction to change as a function of average bottomhole pressure and whether pressure is building up or drawing down, such that the interwell connectivity model is used to characterize the well-to-well interactions by a plurality of flow regimes.
 24. The method of claim 1, wherein the interwell connectivity model, which describes interwell connectivity as a function of pressure, estimates an amount of gas needed to build pressure as a function of injection rate. 